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POLYGRAPHIC SUBSTITUTION SYSTEMS
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CONCLUDING REMARKS
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GLOSSARY
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APPENDIX 5
LETTER FREQUENCY DATA - FOREIGN LANGUAGES
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CRYPTOGRAPHIC SUPPLEMENT
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LESTER S. HILL ALGEBRAIC ENCIEHERMEHT
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COMMUNICATION INTELLIGENCE OPERATIONS
APPENDIX 11
PRINCIPLES OF COMMUNICATION SECURITY
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NATIONAL SECURITY AGENCY
MILITARY CRYPTANALYSIS
Part I
4th Edition
By
WILLIAM F. FRIEDMAN
Revised and enlarged by
LAMBROS D. CALLIMAHOS
National Security Agency
Washington 25, D. C.
December 1952
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The Golden Guess
Is Moming-Star to tbe full round of Truth .
— Tennyson.
Preface to the 4th Edition
This edition represents an extensive expansion and revision of die original
text, in both scope and content, necessitated by the considerable advancement
made in the art since the publication of the previous editions.
1 wish to express grateful acknowledgment for Mr. Friedman’s generous
assistance and invaluable collaboration in the preparation of this edition.
-- L. D. C.
ii
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TABLE OF CONTENTS
MILITARY CRYPTANALYSIS, PART I
Monoalphabctic Substitution Systems
Section Paragraphs Pages
I. Introductory remarks* 1-3 1-10
II* Basic cryptologic considerations * 4-13 11 **20
III* Fundamental cryptanalytic operations 14-20 21-30
IV. Frequency distributions and their
fundamental uses 21-28 31-54
V. Uniliteral substitution with standard
cipher alphabets.. 29-37 55-74
VI. Uniliteral substitution with mixed cipher
alphabets.... 38-51 75-
VII. Multiliteral substitution with s ingle -
equivalent cipher alphabets....... 52 -
VIII. Multiliteral substitution with variants
IX. Polygraphic substitution systems
X. Concluding remarks
APPENDICES
1 .
2 .
3.
4.
5.
6 .
7.
8 .
9.
10 .
11 .
• 12 .
13.
14.
INDEX
Glossary.
Letter frequency data - English
Word and pattern lists - English........
Service terminology; stereotypes
Letter frequency data - foreign languages....
List of frequent words - English and foreign languages.
Cryptographic supplement
Lester S. Hill algebraic encipherment
Open codes and concealment systems...
Communication intelligence operations
Principles of communication security
Bibliography; recommended reading
Problems - Military Cryptanalysis, Part I
Foreign language problems
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INTRODUCTORY REMARKS
Paragraph
Scope of this text 1
Mental equipment necessary for cryptanalybic work 2
Validity of results of cryptanalysis 3
1. Scope of this text .— e . This text constitutes the first of a
series of six basic texts 1 on the art of cryptanalysis . Although most of
the Information contained herein is applicable to cryptograms of various
types and sources, special emphasis will he laid upon the principles and
methods of solving military 2 cryptograms. Except for an introductory
discussion of fundamental principles underlying the science of cryptana-
lytics , this first text in the series will deal solely with the principles
and methods for the analysis of monoalphabet ic substitution ciphers .
Even with this limitation it will be possible to discuss only a few of the
many variations of this one type that are met in practice; but with a
firm grasp upon the general principles few difficulties should be expe-
rienced with any modifications or variations that may be encountered.
b. This and some of the succeeding texts will deal only with basic
types of cryptosystems not because they may be encountered unmodified in
military operations but because their study is essential to an under-
standing of the principles underlying the solution of the modern, very
much more complex types of codes, ciphers, and certain encrypted trans-
mission systems that are likely to be employed by the larger governments
of today in the conduct of their military affairs in time of war.
c . It is presupposed that the student has no prior background in
the field of cryptology; therefore cryptography is presented concurrently
with cryptanalysis. Basic terminology and preliminary cryptologic consi-
derations are treated in Section II; other terms are usually defined upon
their first occurrence , or they may be found in the Glossary (Appendix l) .
d. The cryptograms presented in the examples embrace messages from
hypothetical air, ground, and naval traffic; thus, the student will have
the opportunity to familiarize himself with the language and phraseology
of all three Services comprising the Armed Forces of the United States •
1 Each text has its accompanying course in cryptanalysis, so that the
student may test his learning and develop his skill in the solution of
the types of cryptograms treated in the respective texts. The problems
which pertain to this text constitute Appendix 13.
2 The word "military” is here used in its broadest sense. In this
connection see subpar. d, below.
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2. Mental equipment necessary for eryptanalytic work . — a. Captain
Parker Ilitt, in the first United States Army manual^ dealing with cryp-
tology, opens the first chapter of his valuable treatise with the
following sentences
"Success in dealing with unknown ciphers is measured by these four
things in the order named: perseverance, careful methods of analysis,
intuition, luck."
These words are as true today as they were then. There is no royal
road to success in the solution of cryptograms. Hitt goes on to say:
"Cipher work will have little permanent attraction for one who
expects results at once, without labor, for there is a vast amount of
purely routine labor in the preparation of frequency tables, the rearrange
ment of ciphers for examination, and the trial and fitting of letter to
letter before the message begins to appear."
The present author deems it advisable to add that the kind of work
involved in solving cryptograms is not at all similar to that involved in
solving crossword puzzles, for example. The wide vogue the latter have
had and continue to have is due to the appeal they make to the quite
common interest in mysteries of one sort or another j but in solving a
crossword puzzle there is usually no necessity for performing any preli-
minary labor, and palpable results become evident after the first minute
or two of attention. This successful start spurs the crossword "addict"
on to complete the solution, which rarely requires more than an hour's
time. Furthermore, crossword puzzles are all alike in basic principles
and once understood, there is no more to learn. Skill comes largely from
the embellishment of one’s vocabulary, though, to be sure, constant prac-
tice and exercise of the imagination contribute to the ease and rapidity
with which solutions are generally reached. In solving cryptograms,
however, many principles must be learned, for there are many different
systems of varying degrees of complexity. Even some of the simpler
varieties require the preparation of tabulations of one sort or another,
which many people find irksome; moreover, it is only toward the very close
of the solution that results in the form of intelligible text become
evident. Often, Indeed, the student will not even know whether he is on
the right "rad: until he has performed a large amount of preliminary
"spade work" involving many hours of labor. Thus, without at least a
willingness to pursue a fair amount of theoretical study, and a more than
average amount of patience and perseverance , little skill and experience
can be gained in the rather diff icult art of cryptanalysis . General
Givierge, the author of an excellent treatise on cryptanalysis, remarks
in this connection
"The cryptanalyst 's attitude must be that of William the Silent:
No need to hope in order to undertake, nor to succeed in order to
persevere
3 Hitt, Capt. Parker, Manual for the Solution of Military Ciphers .
Army Service Schools Press. Fort Leavenworth, Kansas, 1916. 2d Edition,
1918. (Both out of print.;
^ Givierge, General Marcel, Cours de Cryptographic , Paris, 1925, p. 301
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b. As regards Hitt's reference to careful methods of analysis,
before one can be said to be a cryptanalyst vorthy of the name it is
necessary that one should have, firstly, a sound knowledge of the basic
principles of cryptanalysis, and secondly, a long, varied, and active
practical experience in the successful application of those principles.
It is not sufficient to have read treatises on this subject. One month's
actual practice in solution is worth a whole year's mere reading of
. theoretical principles. An exceedingly important element of success in
solving the more Intricate cryptosystems is the possession of the rather
unusual mental faculty designated in general terms as the power of in-
i ductive and deductive reasoning. Probably this is an Inherited father
than an acquired faculty; the best sort of training for its emergence,
if latent in the individual, and for its development is the study of
the natural sciences, such as chemistry, physics, biology, geology, and
the like. Other sciences such as linguistics, archaeology, and philology
are also excellent.
c. Aptitude in mathematics is quite important, more especially in
the solution of ciphers and enciphered codes than in codebook reconstruc-
tion, which latter is purely and simply a linguistic problem. Although
in the early days of the emergence of the science of cryptanalytics little
thought was given to the applications of mathematics in this field, many
branches of mathematics and, in particular, probability and statistics,
have now found cryptologic applications. Those portions of mathematics
and those mathematical methods which have cryptologic applications 5 are
known collectively as cryptomathematics .
5 tt is quite important to stress at this point that in professional
cryptologic work the science of cryptanalytics is subordinated to the
art of cryptanalysis, just as in .the world of music the technical virtu-
osity of a great violinist is adjuvant to the expression of music, that
is, the virtuosity is a "tool" for the recovery of the complete musical
"plain text" conceived by the composer. Since the practice of cryptana-
lysis is an art, mathematical approaches cannot always be expected to
yield a solution in cryptology, because art can and must transcend the
cold logic of scientific method. By way of example, an experienced
Indian guide can usually find his way out of a dense forest more readily
than a surveyor equipped with all the refined apparatus and techniques
of his profession. Likewise, an experienced cryptanalyst can generally
find his way through a cryptosystem more readily than a pure mathematician
equipped merely with the techniques of his field no matter how abstruse
or refined they may be . A cryptomathematician of repute once stated
that "the only effect of ^refined mathematical techniqueis7 is frequently
to discourage one so much that one does nothing at all and some unmathe-
matical ignoramus then gets the problem out in some very unethical way.
This is intensely irritating." See also in this connection the remarks
made in subpar. 27 e in reference to the validity of statistical tests
in cryptanalysis.
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d. An active imagination, or perhaps what Hitt and <?ther writers
call intuition , is essential, hut mere imagination uncontrolled by a
judicious spirit will he more often a hindrance than a help. In prac-
tical cryptanalysis the imaginative or intuitive faculties must, in other
words, he guided hy good judgment, hy practical experience, and hy as
thorough a knowledge of the general situation or extraneous circumstances
that led to the sending of the cryptogram as is possible to obtain. In
this respect the many cryptograms exchanged between correspondents whose
identities and general affairs, commercial, social, or political, are
known are far more readily solved® than are isolated cryptograms exchanged
between unknown correspondents, dealing with unknown subjects. It is
obvious that in the former case there We good data upon which the intu-
itive powers of the cryptanalyst can be brought to bear, whereas in the
latter case no such dr>ta are available. Consequently, in the absence of
Buch data, no matter how good the imagination and intuition of the cryp-
tanalyst, these powers are of no particular service to him. Some writers,
however, regard the intuitive spirit as valuable from still another
viewpoint, as may be noted in the following; 7
I •
"Intuition, like a fla,sh of lightning, lasts only for a second.
It generally comes when one is tormented by a difficult decipherment and
when one reviews in his mind the fruitless experiments already tried.
Suddenly the light breaks through and one finds after a few minutes what
previous days of labor were unable to reveal."
• This, too, is true, but unfortunately there is no way in which the
intuition may be summoned at will, when it is most needed.® There are
certain authors who regard as indispensable the possession of a somewhat
6 The application in practical, operational cryptanalysis of "probable
words" or "cribs", i.e., plain text assumed or known to be present in a
cryptogram, is developed in time of war into a refinement the extent and
usefulness of which cannot be appreciated by the uninitiated. Even as
great a thinker as Voltaire found the subject of cryptanalysis stretching
his credulity to the point that he said:
"Those who boast that they can decipher a letter without knowing its
subject matter, and without preliminary aid, are greater charlatans than
those who would boast of understanding a language which they have never
learned." — Dlctionnaire Philos ophique , under the article "Poste" .
7 Lange et Soudart, Traite de Cryptographie, Libraire Felix Alcan,
Paris, 1925 , p. 104 . „ rf '
8 The following extracts are of interest in this connection:
“The fact that the scientific investigator works 50 per cent of his time by non-rational means is, it seems, quite
insufficiently recognized. There is without the least doubt an instinct for research, and often the most successful
investigators of nature are quite unable to give an account of their reasons for doing such and Buch an experi-
ment, or for placing side by side two apparently unrelated facts. Again, one of the most salient traits ip the
character of the successful scientific worker is the capacity for knowing that a point is proved when it would not
appear to be proved to an outside intelligence functioning in a purely rational manner; thus the investigator
feels that some proposition is true, and proceeds at once to the next set of experiments without waiting and wasting
time in the elaboration of the foimal proof of the point which heavier minds would need. Questionless such a
scientific intuition may and docs sometimes lead investigators astray, but it is quite certain that if they did
not widely make use of it, they would not get a quarter as far as they do. Experiments confirm each other, and a
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rare , rather mysterious faculty that they designate by the word "flair” ,
or by the expression "cipher brains" . Even so excellent an authority as
General Givierge , 9 in referring to this mental faculty, uses the fol-
lowing words:
"Over and above perseverance and this aptitude of mind which some
authors consider a special gift, and which they call intuition, or even,
in its highest manifestation, clairvoyance, cryptographic studies will
continue more and more to demand the qualities of orderliness and memory."
Although the present author believes a special aptitude for the
work is essential to cryptanalytic success, he is sure there is nothing
mysterious about the matter at all. Special aptitude is prerequisite to
success in all fields of endeavor. There are, for example, thousands
of physicists, hundreds of excellent ones, but only a handful of world-
wide fame. Should it be said, then, that a physicist who has achieved
very notable success in his field has done so because he is the fortunate
possessor of a mysterious faculty? That he is fortunate in possessing a
special aptitude for his subject is granted, but that there is anything
mysterious about it, partaking of the nature of clairvoyance (if, indeed,
the latter is a reality ) is not granted. While the ultimate nature of
any mental process seems to be as complete a mystery today as it has
ever been, the present author would like to see the superficial veil of
mystery removed from a subject that has been shrouded in mystery from
even before the Middle Ages down to our owe times . (The principal and
readily understandable reason for this is that governments have always
closely guarded cryptographic secrets and anything so guarded soon becomes
"mysterious".) He would, rather, have the student approach the subject
as he might approach any other science that can stand on its own merits
with other sciences, because cryptanalytics, like other sciences, has a
practical importance in human affairs. It presents to the inquiring mind
an interest in its own right as a branch of knowledge; it, too, holds
forth many difficulties and disappointments, and these are all the more
false step is usually soon discovered. And not only by this partial replacement of reason by intuition does the
work of science go on, but also to the born scientific worker — and emphatically they cannot be made — the struc-
ture of the method of research is as it were given, he cannot explain it to you, though he may be brought to agree
a posteriori to a formal logical presentation of the way the method works”. — Excerpt from Needham, Joseph,
The Sceptical Biologist f London, 1929, p. 79.
“The essence of scientific method, quite simply, is to try to see how data arrange themselves into causal
configurations. Scientific problems are solved by collecting data and by “thinking about them all the time.”
We need to look at strange things until, by the appearance of known configurations, they seem familiar, and to
look at familiar things until we see novel configurations which make them appear strange. We must look at
events until they become luminous. That is scientific method . . . Insight is the touchstone . . . The appli-
cation of insight as the touchstone of method enables us to evaluate properly the role of imagination in scientific
method. The scientific process is akin to the artistic process: it is a process of selecting out those elements of
experience which fit together and recombining them in the mind. Much of this kind of research is simply a cease-
less mulling over, and even the physical scientist has considerable need of an armchair . . . Our view of scien-
tific method as a struggle to obtain insight forces the admission that science is half art . . , Insight is the
unknown quantity which has eluded students of scientific method”. — Excerpts from an article entitled Insight and
Scientific Method , by Willard Waller, in The American Journal of Sociology , Vol. XL, 1934*.
9 Op. clt ., p. 302.
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keenly fell when the nature. of these difficulties is not understood hy
those unfamiliar with the special circumstances that very often are the
real factors that led to success in other cases. Finally, just as in
the other sciences wherein men labor long and earnestly for the true
satisfaction and pleasure that comes from work well done, so the mental
pleasure that the successful cryptanalyBt derives from his accomplish-
ments is very often the only reward for much of the drudgery that he must
do in his daily work. General Givierge's words in this connection are
well worth quoting: 10
"Some studies will last for years before bearing fruit. In the case
of others, cryptanalysts underbaking them never get any result. But, for
a cryptant l /at who likes the work, the Joy of discoveries effaces the
memory of bis hours of doubt and impatience."
o. Willi his usual deft touch, Hitt says of the element of luck, as
regards the role it plays in analysis:
"As to luck, there is the old miners’ proverb: 'Gold is where you
find it.’"
The cryptanalyst is lucky when one of the correspondents whose cryp-
tograms he is studying makes a blunder that gives the necessary clue; or
when he finds two cryptograms identical in text but in different keys in
the same system; or when he finds two cryptograms identical in text but
in different systems, and so on. The element of luck is there, to be
sure, but the cryptanalyst must be on the alert if he is to profit by
these lucky ‘'breaks". ~
f . If the present author were asked to state, in view of the pro- •
gress”in the field since 1916, what elements might be added to the four
ingredients Hitt thought essential to cryptanalytic success, he would
be inclined to mention the following:
(1) A broad, general education, embodying interests covering as
many fields of practical knowledge as possible. This is useful because
the cryptanalyst is often called upon to solve messages dealing with
the most varied _r human activities, and the more he knows about these
activities, the easier his task.
(2) Access- to a large library of current literature, and wide and
direct contacts with sources of collateral information. These often'
afford clues afe to the contents of specific messages. For example,, to
be able instantly to have at his disposal a newspaper report or a
personal report of events described or referred to in a message under
investigation goes a long way toward simplifying or facilitating
solution. Government cryptanalysts are sometimes fortunately situated
in this respect, especially where various agencies work in harmony.
(3) Proper coordination of effort. This includes the organization
of cryptanalytic personnel into harmonious, efficient teams of cooperating
individuals .
1° Op. cit ., p. 301.
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(!») Under mental equipment be would also include tbe faculty of
being able to concentrate on a problem for rather long periods of time,
without distraction, nervous irritability, and impatience . The strain
under which cryptanalytic studies are necessarily conducted is quite
severe and too long -continued application has the effect of draining
nervous energy to an unwholesome degree, so that a word or two of caution
may not here he out of place. One should continue at work only so long
as a peaceful, calm spirit prevails, whether the work is fruitful or not.
But just as soon as the mind becomes wearied with the exertion, or just
as soon as a feeling of hopelessness or mental fatigue intervenes, it is
better to stop completely and turn to other activities, rest, or play.
It is essential to remark that systematization and orderliness of work
are aids in reducing nervous tension and irritability. On this account
it is better to take the time to prepare the data carefully, rewrite the
text if necessary, and so on, rather than work with slipshod, incomplete,
or improperly arranged material.
(5) A retentive memory is an important asset to cryptanalytic skill,
especially in the solution of codes. The ability to remember individual
groups, their approximate locations in other messages, the associations
they form with other groups, their peculiarities and similarities, saves
much wear and tear of the mental machinery, -as well as much time in
looking up these groups in indexes .
(6) The assistance of machine aids in cryptanalysis. The importance
and value of these aids cannot be overemphasized in their hearing on prac-
tical, operational cryptanalysis, especially in the large-scale effort
that would be made in time of war on complex, high-grade cryptosystems at
a theater headquarters or in the zone of the interior. These aids, under
the general category of rapid analytical machines, comprise both punched-
card tabulating machinery and certain other general- and special-purpose
high-speed electrical and electronic devices. Some of the more compact
equipment may be employed by lower echelons within a theater of operations
to facilitate the cryptanalysis of medium-grade cryptosystems found in
tactical communications .
g. It may he advisable to add a word or two at this point to prepare
the student to expect slight mental jars and tensions which will almost
inevitably come to him in the conscientious study of this and the sub-
sequent texts. The present author is well aware of the complaint of
students that authors of texts on cryptanalysis base much of their expla-
nation upon their foreknowledge of the "answer" —which the student does
not know while he is attempting to follow the solution with an unbiased
mind. They complain, too, that these authors use such expressions as "it
is obvious that", "naturally", "of course", "it is evident that", and
so on, when the circumstances seem not at all to warrant their use.
There is no question that this sort of treatment is apt to discourage
the student, especially when the point elucidated becomes clear to him
only after many hours' labor, whereas, according to the hook, the author
noted the weak spot at the first moment’s inspection. The present
author can only promise to try to avoid making the steps appear to be
much more simple than they really are, and to suppress glaring instances
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of unjustifiable "jumping at conclusions". At the same time he must
indicate that for pedagogical reasons in many cases a message has been
consciously "manipulated" so as to allow certain principles to become
more obvious in the illustrative examples than they ever are in practical
work. During the course of some of the explanations attention will even
be directed to cases of unjustified inferences . Furthermore , of the
student who is quick in observation and deduction, the author will only
ask that he bear in mind that if the elucidation of certain principles
seems prolix and occupies more space than necessary, this is occasioned
by the author's desire to carry the explanation forward in very short,
easily-comprehended, and plainly-described steps, for the benefit of
students who are perhaps a bit slower to grasp but who, once they under-
stand, are able to retain and apply principles slowly learned just as
well, if not better than the students who learn more quickly.-'--'-
3. Validity of results of cryptanalysis .--Valid or authentic
cryptanalytic solutions cannot and do not represent "opinions" of the
cryptanalyst. They are valid only so far as they are wholly objective,
and are susceptible of demonstration and proof, employing authentic,
objective methods. It should hardly be necessary (but an attitude fre-
quently encountered among laymen makes it advisable) to indicate that
the validity of the results achieved by any serious cryptanalytic studies
on authentic material rests upon the same sure foundations and are
reached by the same general steps as the results achieved by any other
scientific studies; viz. , observation, hypothesis, deduction and induction,
and confirmatory experiment. Implied in the latter is the possibility
that two or more qualified investigators, each working independently
upon the same material, will achieve identical (or practically identical)
results — there is one and only one (valid) solution to a cryptogram.
Occasionally a "would-be" or pseudo-cryptanalyst offers "solutions" which
cannot withstand such tests; a second, unbiased, investigator working
independently either cannot consistently apply the methods alleged to
have been applied by the pseudo-cryptanalyst, or else, if he can apply
In connection with the use of the word "obvious", the following
extract is of interest:
"Now the word 'obvious' is a rather dangerous one. There is an
incident, vhieh has become something of a legend in mathematical circles,
that illustrates this danger. A certain famous mathematician was lec-
turing to a group of students and had occasion to use a formula which he
wrote down with the remark, 'This statement is obvious . ' Then he paused
and looked rather hesitantly at the formula. 'Wait a moment, ' he said.
'Is it obvious? I think it's obvious.' More hesitation, and then,
'Pardon me, gentlemen, I shall return.* Then he left the room. Thirty-
five minutes later he returned; in his hands was a sheaf of papers
covered with calculations, on his face a look of quiet satisfaction.
*1 was right, gentlemen. It is obvious,' he said, and proceeded with his
lecture." — Excerpt from The Anatomy of Mathematics by Kershner and Wilcox.
New York, 1950.
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them at all, the results (plaintext translations) are far different in
the two cases. The reason for this is that in such cases it Is generally
found that the "methods", are not clear-cut, straightforward or mathema-
tical in character. Instead, they often involve the making of judgments
on matters too tenuous to measure, weigh, or otherwise subject to careful
scrutiny. Often, too, they involve the "correction" of an inordinate
number of "errors" which the pseudo -cryptanalyst assumes to he present and
which he "corrects" in order to make his "solution" intelligible. And
sometimes the pseudo -cryptanalyst offers as a "solution" plain text which
is intelligible only to him or which he makes intelligible by expanding
what he alleges to be abbreviations, and so on. In all such cases, the
conclusion to which the unprejudiced observer is forced to come is that
the alleged "solution" obtained by the pseudo-cryptanalyst is purely
subjective In nearly all cases where this has happened (and they occur
from time to time) there has been uncovered nothing which can in any way
12 a mathematic ian is often unable to grasp the concept behind the ex-
pression "subjective solution" as used in the cryptanalytic field, since
the idea is foreign to the basic philosophy of mathematics and thus the
expression appears to him to represent a contradiction in terms. As an
illustration, let us consider a situation in which a would-be cryptanalyst
offers a solution to a cryptogram he alleges to be a simple monoalphabetic
substitution cipher. His so-called solution, however, requires that he
assume the presence of, let us say, approximately 50 $ garbles (which he
claims to have been introduced by cipher clerks’ errors, faulty radio
reception because of adverse weather conditions, etc.). That is, the
"plain text" he offers as the "solution" involves his making helter-
skelter many "corrections and emendations", which, one maybe sure, will
be based on what his subconscious mind expects or desires to find in the
cleartext message. Unfortunately, another would-be cryptanalyst working
upon the same cryptogram and hypothesis independently might conceivably
"degarble" the cryptogram in different spots and produce an entirely
dissimilar "plain jbext" as his "solution" . Both "solutions" would be
invalid because they are based upon an erroneous hypothesis — the crypto-
gram actually happens to be a polyalphabetic substitution cipher which
when correctly analyzed requires on the part of unbiased observers no
assumption of garbles to a degree that strains their credulity. The
last phrase is added here because in professional cryptanalytic work it
is very often necessary to make a few corrections for errors but it is
rarely the case that the garble rate exceeds more than a few percent of
the characters of th^ cryptogram, say 5 to 10$ at the outside. It is
to be noted, however, that occasionally the solution to a cryptogram
may Involve the correction of more than this percentage of errors, but
the solution would be regarded as valid only if the errors can be shown
to be systematic in some significant respect, or can otherwise be
explained by objective rationalization.
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REF ID: A5 68 95
"be used to impugn the integrity of the pseudo-crypts nalyst . The worst
that can he said of him ic that La has become a victim of a special or
peculiar form of self-delusion, and that his desire to solve the problem,
usually in accord with some previously-formed opinion, or notion, has
over -balanced, or undermined, his judgment and good sense .^3
Specific reference can be made to the following typical ’’case
histories" :
Donnelly, Ignatius, The Great Cryptogram . Chicago, 1888.
Owen, Orville W., Sir Francis Bacon's Cipher Story . Detroit, 1895*
Gallup, Elizabeth Wells, Francis Bacon's Biliteral Cipher *
Detroit, 1900.
Arensborg-, Walter Conrad, The Cryptography of Shakespeare . Los
Angeles, 1922.
The Shakespearean Mystery . Pittsburgh, 1928. v
The Baconian Keys . Pittsburgh, 1928.
Margoliouth, D. S., The Homer of Aristotle . Oxford, 1923*
Newbold, William Romaine, The Cipher of Roger Bacon . Philadelphia,
1928. t(For a scholarly and complete demolition of Professor
Newbold'' s work, see an article entitled Roger Bacon and the
Voynich 'MS, by John M. Manly, in Speculum, Vol. VI, No. 3,
July 1931.)
Feely, JoBeph Martin, The Shakespearean Cypher . Rochester, N. Y.,
1931.
Deciphering Shakespeare . Rochester, N. Y., 193^ •
koger Bacon’s Cypher: the right key found . Rochester, N. Y., 19^3*
Wolff, Werner, Dlchiffrement de l'Ecriture Maya . Paria, 1938.
Strong, Leonell C., Anthony Askham, the author of the Voynich
manuscript , in Science , Vol. 101, June 1$, 19^5 , PP. 608-9.
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10
REF ID : A56895
HEDTRICTE&
SECTION II
BASIC CKXFTGLOGIC CONSIDERATIONS
Cryptology, communication intelligence, and communication
security e ***»*****•*«*«*•• »**-**»**«-»*. ***4-****tf*4^****aa
Paragraph
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...... *
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CrVDtOd , &'Dh‘V’ a encrvntinfif A anfl. Ae(5!l*VDtlllXf A -**»*a* **************
...... 7
Godina * olnTiAVri * smfl Avtrt'f'nhoivkA aa/Ia . . u . , . . . , .i.
fl
ftftRftMl avaf.Ain * a Vav _ nnri Awm+.nsvn+.Aiti 0
Cl^Yotanalvt ic a cifvotanalvfiis
A A A A * A jQ
TranSDOfiltiOn a-tlfl SUb S t ittlt ion -
Kcfbure of alphabet a
...... ’■ is
Types of alphabets *
4. Cryptology* communication Intelligence « and communication
aecurlty . Ime oeeaSSSnaT or frequent peed for secrecy Ini the conduct of
important affairs has been recognized from time Immemorial* In the case
of diplomacy and organized warfare this need Is especially Important In
regard to communications* . However, when such communications are trans-
mitted by electrical means, they can be heard and copied by unauthorized
persons* The protection resulting from, all measures designed to deny
to unauthorized persons information of value which may be derived from
such communications Is called communication security . The evaluated
Information concerning the enemy, derived principally from a study of his
electrical communications, is called communication intelligence * The col-}
lective term Including all phases of communication intelligence and com-
munication security is cryptology .3- Or, stated in broad terms, cryptology
is that branch of knowledge which treats of hidden, disguised, or secret^
communications *
A From the Greek kryptos (hidden) 4* logos (learning)* The prefix
"crypto-" in compound words pertains to ^cryptologic", "cryptographic".
Or "crypt analytic" , depending upon the use of the particular .word as
defined*
2 In this text the term "secret" will be used in its ordinary sense
as given in the dictionary* Whenever the designation is used in the more
restricted sense of the security classification as defined in official
regulations, it will be capitalized. There are In current use the four
classifications Restricted. Confidential. Secret, and Top Secret, listed
in ascending order of degree.
REOTRICTEP
11
REF ID: A5 68 95
riEauur'H se-
5» Secret coiiin)mlcation »«»«a. Communication may “be conducted by
any me axis susceptible oS ultimate interpretation by one of the five
senses, but those most commonly used are sight and bearing. Aside from
the use of simple visual and auditory signals for communication over
relatively short distances, the uaual method of communication between
or among individuals separated from one another by relatively long dis-
tances involves, at one stage or another, the act of writing or of
speaking over a telephone.
b. Privacy or secrecy in communication by telephone can be obtained
by using equipment which affects the electrical currents Involved in te-
lephony so that the conversations can he understood only by persons pro-
vided with suitable equipment properly arranged for the purpose. The
same thing is true in the case of electrical transmission of pictures,
drawings, maps, and television Images* However, this t eat will not treat
of these aspects3 of cryptology.
c. Writing may be either visible or invisible . In the former, the
characters are inscribed with ordinary writing materials and can be seen
with the naked eye; in the latter, the characters are inscribed by means
or methods which make the writing Invisible to the naked eye. Invisible
writing can be prepared with certain chemicals called invisible, sympa-
thetic, or secret inks, and in order to "develop" such writing, that is,
make It visible, special processes must usually be applied. There are
also methods of producing writing which is invisible to the naked eye
because the characters are of microscopic size, thus requiring special
photographic or microscopic apparatus to make such writing visible to the
naked eye.
d. Invisible writing and unintelligible visible writing constitute
secreF writing .
6. Plain teacfc and encrypted text *— a. Visible writing which is
intelligible, that is, conveys a more or Tees understandable or sensible
meaning (in the language in which written) and which is not intended to
convey a hidden meaning, is said to be in plain text . 1 * A message in
plain text is termed a plaintext message, a cleartext message, or a
mea sage in clear.
3 These aspects of cryptology are now known as ciphony (from cipher +
tele phony) ; clfax (from cip her + facsi mile); and clviBlon (from cipher +
tel evision) •
^ Visible writing may be Intelligible but the meaning It obviously
conveys may not be its real meaning, that is, the meaning intended to be
conveyed. To quote a simple example of an apparently innocent message
containing a secret or hidden meaning, prepared with the intention of es-
c aping censorship, the sentence "Son bom today" may mean "Three trails-''
ports left today." Messages of this type are said to be In open code. -
Secret communication methods or artifices of this sort (concealment sys-
tems) are impractical for field military use but are often encountered
in espionage and counter-espionage activities .
REffTIilCTE fr
12
REF ID : A56895
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b. visible -writing -which conveys no intelligible meaning In any
recognized language? is said to be In encrypted text and such writing la
termed a cryptogram .”
7» Cryptography , e ncryptin g, a nd dec rypting , —a. Cryptography I®
that branch of crOTwlogy'wnich treats oFvaxfous means/ Toeth^s, am
apparatus for con-verting or transforming plaintext messages into crypto-
grams and for reconverting the cryptograms into their original plaintext
forms by a sinple reversal of the steps used in their transformation.
b. To encrypt la to convert or transform a plaintext message into
a cryptogram by following certain rules, steps, or processes constituting
the key or keys and agreed upon in advance by correspondents, or furnished
them by higKer authority*
c. To decrypt is to reconvert or to transform a cryptogram into the
original equivalent' plaintext message by a direct reversal of the en-
crypting process, that is, by applying' to the cryptogram the key or keys
\ dually in a" reverse order) ^used. in producing the cryptogram*
d . A person skilled in the’ art of encrypting and decrypting, or one
who has a part in devising a cryptographic system is called a crypto-
grapher; a clerk who encrypts and decrypts, or who assists in such work,
is called a cryptographic clerk .
8. Codes, ciphers, a nd enciphered code .— a. Encrypting and de-
crypting are accoiiplished^y means c ollec£ively r ’ designated as codes and
ciphers . Such means are used for either or both of two purposes: (1) se-
crecy, and (2) economy or brevity. Secrecy usually is far more Important
in military cryptography than economy or brevity. In ciphers or cipher
systems* cryptograms are produced by applying the cryptographic treatment
to "individual letters of the plaintext messages, whereas, in codes or code
systems, cryptograms are produced by applying the cryptographic treatment
to entire words, phrases, and sentences of the plaintext messages. The
specialized meanings of the terms code and cipher are explained in detail
later.
b. A cryptogram produced by means of a cipher system is said to be
in cipher and is called a cipher message, or sometimes sitply a cipher .
®J&e act or operation of encrypting a cipher message is called enciphering,
* There is a certain type of writing which is considered by its authors
to be intelligible, but which is either completely unintelligible to the
wide variety of readers or else requires considerable mental struggle on
their part to make it intelligible. Reference is here made to so-called
"modern literature" and "modem verse", products of such writers as
E. E. Cummings, Gertrude Stein, James Joyce, et al.
’ ^ From kryptos + gramma (that which is written). Analogous terminol-
ogy would call' 'a' plaintext message a phanerogram ( phaneros 3 visible,
manifest, open).
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13
REF ID: A5 68 95
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and the enciphered version of the plain test, as veil as the act or pro-
cess itself, is often referred to as the encipherment * The cryptographic
clerk vho performs the process serves as an encipherer * The corresponding
terms applicable to the decrypting of cipher messages are deciphering*
decipherment* and decipherer * A clerk vho serves as both an encipherer
ancT decipherer of messages is called a cipher clerk *
c. A cipher device is a relatively simple mechanical contrivance for
encipHermenb and decipherment, usually "hand-operated" or manipulated by
the fingers, as for example a device vith concentric rings of alphabets,
manually povered; a cipher machine is a relatively complex apparatus or
mechanism for encipherment and decipherment, usually equipped with a
typewriter key board and often requiring an external power source.
d* A cryptogram produced by means of a code system is said to be In
code and is called a code message . The text of the cryptogram is referred
to as code text . This act or operation of encrypting is called encoding*
and the encoded version of the plain text, as well as the act or process
Itself, is referred to as the encodement . The clerk who performs the pro-
cess serves as an encoder . The corresponding terms applicable to the
decrypting of code messages are decoding* decodement* and decoder . A
cryptographic clerk who serves as both an encoder and decoder of messages
is called a code clerk .
e. Sometimes, for special purposes (usually increased security),
the ccTde text of a cryptogram undergoes a further step in concealment
involving superencryption , that is, encipherment of the characters com-
prising the code text, thus producing what is called an enciphered-oode
message* or enciphered code . Encoded cipher, that is, the case where the
filial cryptogram is produced by enciphering the plain text and then en-
coding the cipher text obtained from the first operation, is also possible,
but rare.
9. General system* specific key* and cryptosystem .— a. There are
a great many different methods of emr^tihg messages, so that correspon-
dents must first of all be in complete agreement as to which of them will
be used in their secret communications, or in different types or classes
of such communications. Furthermore, it is to be understood that all the
detailed rules, processes, or steps comprising the cryptography agreed
Upon will be invariant* that is, constant or unvarying in their use in a
given set of communications. The totality of these basic, invariable
rules, processes, or steps to be followed in encrypting a message according
to the agreed method constitutes the general cryptographic system or, more
briefly, the general system .
b. It is usually the case that the general system operates in con-
nection with or under the control of a number, a group of letters, a word,
a phrase, or sentence which is used as a key* that is, the element which
specifically governs the manner in which the general system will be applied
in a specific message, or the exact setting of a cipher device or a cipher
machine at the initial point of encipherment or decipherment of a specific
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14
REF ID: A5 68 95
• REDTRICTED ■
message. This element — usually of a variable nature or changeable at the
will of the correspondents, or prearranged for them by higher authority—
Is called the specific key . The specific key may also Involve the use of
a set of specially prepared tables, a special document, or even a book.
£. The term cryptosystem? is used when It Is desired to designate
or refer to all the cryptomaterial (device, machine, Instructions for use,
key lists, etc.) as a unit to provide a single, complete system and means
for secret communication.
10. Gryptanalytlc s and cryptanalysis .— a. In theory any cryptosystem
(except one**) can be "broken", l.e., solved, If enough time, labor, and
skill are devoted to It, and if the volume of traffic in that system Is '
large enough. This can be done even if the general system and the sped*
fic key are unknown at the start. In military operations theoretical
rules must usually give way to practical considerations. How the theo-
retical rule in this case Is affected by practical considerations will
be discussed in Appendix 11.
b. That branch of cryptology which deals with the principles,
methods, and means employed in the solution or analysis of cryptosystems
is called cryptanalytics .
c. The steps and operations performed in applying the principles of
cryptanalytics constitute cryptanalysis . To cryptanalyze a cryptogram
is to solve it by cryptanalysis.
11. Transposition and substitution .— a. Technically there are only
two distinct types' of' treatment which! may Fe applied to written plain
text to convert it into secret text, yielding two different classes of
cryptograms. In the first, called transposition, the elements or units
of the plain text retain their original identities and merely undergo
some change in their relative positions, with the result that the original
text becomes unintelligible . In the second, called substitution, the
elements of the plain text retain their original relative positions but
are replaced by other elements with different values or meanings, with
the result that the original text becomes unintelligible. Thus, in the
case of transposition ciphers, the unintelligibility is brought about
merely by a change in the original sequence of the elements or units of
Y The term cryptosystem is used in preference to cryptographic system
so as to permit its use in designating secret communication' systems
involving means other than writing, such as clphony and clfax.
®..The exception is the "one-time” system in Which the key is used only
once and in itself must have no systematic construction, derivation, or
meaning.
RESTRICT E B
15
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REF ID : A56895
the plain text; In the case of substitution ciphers, the unintelllgi-
bility is brought about by a change in the elements or units themselves,
■without a change in their relative order*
b* It is possible to encrypt a message by a substitution method and
then to apply a transposition method to the substitution text, or vice
versa* Such combined transposition-substitution methods do not form a
third class of methods* They are occasionally encountered in military
cryptography, but the types of combinations that are sufficiently simple
to be practicable for field vise are very limited *9 _
c. Under each of the two principal classes of cryptograms as out-
Uned*~above, a further classification can be made based upon the number
of characters composing the textual elements or units undergoing crypto-
graphic treatment. These textual units are composed of (1) individual
letters, (2) combinations of letters in regular groupings, (3) combina-
tions of letters in Irregular, more or less euphonious groupings called
syllables, and (4) complete words, phrases, and sentences* Methods which
deal with the first type of units are called monographic methods; those
which deal with the second type are called polygraphia ( digraphic , trl-
grephic, etc*); those which deal with the third type, or syllables, are
called syllabic; and, finally, those which deal with the fourth type are
called lexical (of or pertaining to words)*
d* It is necessary to indicate that the foregoing classification of
cryptographic methods is more or less artificial in nature, and is estab-
lished for purpose of convenience only. No sharp line of demarcation can
be drawn in every case, for occasionally a given system may combine me-
thods of treating single letters, regular or irregular-length groupings
of letters, syllables, words, phrases, and complete sentences* When in
a single system the cryptographic treatment is applied to textual units
of regular length, usually monographic or digraphic (and seldom longer,
or intermixed monographic and digraphic), the system is called a cipher
system . Likewise, when in a single system the cryptographic treatment is
applied to textual units of irregular length, usually syllables, whole
words, phrases, and sentences, and is only exceptionally applied to single
letters or regular groupings of letters, the system is called a code
system and generally involves the use of a code book . 10
12* Nature of alphabets .— a. One of the simplest kinds of cubstitu-
tlon ciphers is that which is Known in cryptologic literature as Julius
Caesar* s Cipher, but fthlch, as a matter of fact, was a favorite long
before his day* In this cipher each letter of the text of a message is
replaced by the letter standing the third to the right of it in the
9 one notable exception is the ADFGVX system, used extensively by the
Germans in World War I* See in this connection the Cryptographic
Stpplement (Appendix 7) •
10 A list of single letters, frequent digraphs, tri graphs, syllables,
and words is often called a syllabary; cryptographic treatment of the
units of such syllabaries places ■them in the category of code systems*
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16
REF ID: A5 68 95
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ordinary alphabet; the letter A is replaced by D, the letter B by E,
and so on. The word cab becomes converted into FDE, which is cipher.
b. The English language is written by means of 26 simple characters
called letters which, taken together and considered as a sequence of
symbols'/ ' constitute the alphabet of the language. Not all systems of
writing are of this nature. Chinese writing is contposed of about Mj-, 000
complex characters, each representing one sense of a word. Whereas
English words are composite or polysyllabic and may consist of one to
eight or more syllables, Chinese words are all monosyllables and each
monosyllable is e word. Written languages of the majority of other
civilized peoples of today are, however, alphabetic and polysyllabic in
construction, so that the principles discussed here apply to all of them.
£» The letters comprising the English alphabet used today are the
results of a long period of evolution, the complete history of which may
never fully be known. 11 They are conventional symbols representing
elementary sounds, and any other simple symbols, so long as the sounds
which they represent are agreed upon by those concerned, will serve the
purpose equally well. If taught from early childhood that the symbols
$, *, and @ represent the sounds “Ay", "Bee", and "See" respectively, the
combination @$* would still be pronounced cab, and would, of course, have
exactly the same meaning as before. Again, let us suppose that two per-
sons have agreed to change the sound values of the letters F, G, and H,
and after long practice have become accustomed to pronouncing them as we
pronounce the letters A, B, and C, respectively; they would then write
the "word" HPG, pronounce it cab, and see nothing strange whatever in the
matter. But to others no party to their arrangements, BFG constitutes
cipher. The combination of sounds called for by this combination of
symbols is perfectly intelligible to the two who have adopted the new
sound values for those symbols and therefore pronounce HFG as cab; but
HPG is utterly unpronounceable and wholly unintelligible to others who
are reading it according to their own long-established system of sound
and symbol equivalents. It would be stated that there is no such word
as BFG, which would mean merely that the particular combination of sounds
represented by this combination of letters has not been adopted by con-
vention to represent a thing or an idea in the English language. Thus,
it is seen that, in order for the written words of a language to be
pronounceable and intelligible to all who speak that language, it is
necessary, first, that the sound values of the letters or symbols be
universally understood and agreed upon and, secondly, that the particular
combination of sounds denoted by the letters should have been adopted to
represent a thing or an idea. Spoken plain language consists of vocables;
that is, combinations and permutations of elementary speech-sounds which
have by long usage come to be adopted and recognized as representing
definite things and ideas. Written plain language consists of words;
that is, combinations and permutations of simple symbols, called letters,
which represent visually and call forth vocally the elementary speech-
sounds of which the spoken language is composed.
n 4
An excellent and most authoritative book on this subject is The Al-
phabet; a key to the history of Mankind by David Diringer. London, lykty*
REF ID : A56895
- RESTRICTED -
d. It Is clear also that In order to -write a polysyllabic language
with Facility it is necessary to establish and to maintain by common
agreement or convention, equivalency between two sets of elements, first,
a set of elementary sounds and, second, a set of elementary symbols to
represent the sounds. -When this is done the result is what is called an
alphabet, a word derived from the names of the first two letters of the
Greek alphabet, "alpha” and "beta".
e. Theoretically, in an ideal alphabet each symbol or letter would
denote only one elementary sound, and each elementary sound would inva-
riably be represented by the same symbol. But such an alphabet would be
far too difficult for the average person to use. It has been conserva-
tively estimated that a minimum of 100 characters would be necessary for
English alone. Attempts toward producing and introducing into usage a
practical, scientific alphabet have been made, one being that of the
Simplified Spelling Board in 1928, which advocated a revised alphabet of
42 characters* Were such an alphabet adopted into current usage, in
books, letters, telegrams, etc., the flexibility of cryptographic systems
would he considerably extended and the difficulties set in the path of
the enemy cryptanalysts greatly increased. The chances for its adoption
in the near future are, however, quite small. Because of the continually
changing nature of every living language, it is doubtful whether an
initially "perfect alphabet" could, over any long period of time, remain
so and serve to indicate with great precision the exact sounds which it
was originally designed to represent.
13 . Types of alphabets .— a. In the study of cryptography the dual
nature' of the alphabet becomes*”apparent. It consists of two parts or
components, (l) an arbitrarily-arranged sequence of sounds, and (2) an
arbitrarily-arranged sequence of symbols.
b. The normal alphabet for any language is one in which these two
components are the' ordinary' sequences that have been definitely fixed by
long usage or convention. The dual nature of our normal or everyday
alphabet is often lost sight of. When we write A, B, C,... we really
mean:
Sequence of sounds: "Ay" "Bee" "See" ....
Sequence of symbols: A B C ....
Normal alphabets of different languages vary considerably in the number
of characters composing them and the arrangement or sequence of the
characters. The English, Dutch, and German alphabets each have 26 ; the
French. 25; the Italian, 21; the Spanish, 27 (including the digraphs CH
and Ii); and the Russian, 31 . - 1 - 2 The Japanese language has a syllabary
consisting of 72 syllabic sounds which require 48 characters for their
representation.
In contrast to the foregoing alphabets, it is of interest to note
that in the Hawaiian language the alphabet consists of only 12 letters,
viz , the five vowels A, E, I, 0, U, and the seven consonants H, K, L,
M, N, P, W.
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18
REF ID : A568 95
REF ID: A5 68 95
RE S TRICTED
SECTION III
FUNDAMENTAL CRIFTANALKEIC OPERATIONS
Paragraph
The role of cryptanalysis in communication Intelligence
operations * l4
The four basic operations in cryptanalysis 1?
The determination of the language employed.. 1 6
The determination of the general system..... 17
The reconstruction of the specific ke^. 18
The reconstruction of the plain text..!. ••••• 19
The utilization of traffic intercepts J 20
l4. The role of cryptanalysis in communication intelligence
operations . — a." Through the medium of cozmnunication intelligence an at-
tempt is made""to answer three questions concerning enemy communications:
"Who?" "Where?” "What?" — Who are their originators and addressees?
Where are these originators and addressees located? What do the messages
say?
b. All of the foregoing' questions are very important in the military
application of communication intelligence'. Hence, even though this text
deals almost exclusively with the principles and operations involved in
deriving the answer to the third question — "What do the messages say?" —
a few words on the importance of the first and second questions may be
useful. _It is a serious mistake to thick that one can necessarily and
always correctly Interpret the mere text of a message without identifying
and locating the originator and the addressee or, on many occasions, with-
out having a background against which to interpret the message in order
to appreciate its real import or significance.
£. The very first step in the series of activities involved in de-
riving communication intelligence is the collection of the raw material,
that is, the interception^ - and copying of the transmissions constituting
the messages to be studied and analyzed.
d. Then, with the raw material in hand, studies are made in order
to answer the first two questions — "Who?" and "Where?" The answers to
these questions are not always obvious in modern military communications,
especially in the case of messages exchanged by units in the combat zone,
since messages of this sort rarely Indicate in plain language who the
1 Intercept means, in its cryptologic sense, to gain possession of
communications which are intended for other recipients, without obtaining
the consent of these addressees and without preventing or ordinarily
delaying the transmission of the communications to them.
21
REF ID: A5 68 95
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originator and the addressee are or vfaere they are located. Consequently,
certain apparatus and techniques specifically developed for finding the
answers to these questions must he employed. These apparatus and tech-
niques are embraced by that part of communication intelligence theory and
practice which is known as traffic analysis . This latter subject and
interception are treated briefly in Appendix 10, "Communication intelli-
gence operations” . (The serious student will derive much practical
benefit from a careful reading of this appendix.)
e. The foregoing operations, interception and traffic analysis,
along"" with cryptanalysis constitute the first three operations of commu-
nication intelligence. But generally there must follow at least one addi-
tional operation. If the plain texts recovered through cryptanalysis are
in a foreign language, they must usually be translated, and translation
constitutes this fourth operation. In the course of translating, it may
be found that, because of errors in transmission or reception, corrections
and emendations must be made in these plain texts; however, although this
often requires skill and experience of a high order, it does not consti-
tute another communication intelligence operation, since it is but an
auxiliary step to the process of translation.
f . In a large-Bcale communication intelligence effort these four
steps7 interception, traffic analysis, cryptanalysis, and translation,
must be properly organized and coordinated in order to gain the most bene-
fit from the potentialities of communication intelligence, that is, the
production of the maximum quantity of information from the raw traffic .
This information must then be evaluated by properly trained intelligence
specialists, collated with intelligence derived from other sources, and,
finally, disseminated to the commanders who need the intelligence in time
to be of operational use to them, rather than of mere historical interest.
The foregoing operations and especially the first three— interception,
traffic analysis, and cryptanalysis— usually complement one another.
This, however, is not the place for elaboration on the interrelationships
which exist and which when properly integrated make the operations as a
whole an efficient, unified complex geared to the fulfillment of its prin-
cipal goal, namely, the production of timely communication intelligence.
g. With the foregoing general background, the student is prepared
to proceed to the technical considerations and principles of cryptanalysis.
15. The four basic operations in cryptanalysis .— a. The solution of
practically every cryptogram involves four fundamental operations or steps:
(1) The determination of the language employed in the plaintext
version.
(2) The determination of the general system of cryptography employed.
( 3 ) The reconstruction of the specific key in the case of a cipher
system, or the reconstruction, partial or complete, of the code book, in
the case of a code system; or both, in the case of an enciphered code
system.
( 4 ) The reconstruction or establishment of the plain text.
22
REF ID: A5 68 95
b . These operations will be taken up in the order in which they are
given - * above and in which they usually are performed in the solution of
cryptograms, although occasionally the second step may precede the first
l6. The determination of the language employed * — a. There is not
much that need be said with respect to this operation except that the
determination of the language employed seldom comes into question in the
case of studies made of the cryptograms of an organized enemy. By this
is meant that during wartime the enemy is of course known, and it follows,
therefore, that the language he employs in his messages will almost cer-
tainly be his native or mother tongue . Only occasionally nowadays is
this rule broken. Formerly it often happened, or it might have indeed
been the general rule, that the language used in diplomatic correspondence
was not the mother tongue, but French. In isolated instances during
World War I the Germans used English when their own language could for
one reason or another not be employed. For example, for a year or two
before the entry of the United States into that war, during the time
America was neutral and the German Government maintained its embassy in
Washington, some of the messages exchanged between the Foreign Office in
Berlin and the Enflbassy in Washington were encrypted in English, and a
copy of the code used was deposited with the Department of State and our
censor. Another instance is found in the case of certain Hindu conspira-
tors who were associated with and partially financed by the German Govern-
ment in 1915 and 1916 } they employed English as the language of their
cryptographic messages . Occasionally the cryptograms of enemy agents may
be in a language different from that of the enemy. But in general these
1 Although the foregoing four steps represent the classical or ideal
approach to cryptanalysis, the art may be reduced to the following:
Procedures in crypt anal}
1. Arrangement and rearrangement of
data to disclose non-random cha-
racteristics or manifestations
(i.e., in frequency counts, re-
petitions, patterns, symmetrical
phenomena, etc .) .
2. Recognition of the non -random
characteristics or manifestations
when disclosed.
3. Explanation of the non-random
characteristics when recognized.
Requirements
Experience or ingenuity,
and time (which latter may
be appreciably lowered by
the use of machine aids in
cryptanalysis) .
Experience or statistics.
Experience or Imagination,
and intelligence.
In all of the foregoing, the element of luck plays a very important part,
as it is possible to side-step a large amount of labor and effort, in
many cases, if "hunches" or intuition lead the analyst forthwith to the
right path. Therefore, the phrase "or luck" should be added to each of
the requirements above.
In fact, it all boils down to the simple statement: "Find something
significant, and attach some significance thereto."
23
REF ID: A5 68 95
are, as has been said, isolated instances? as a rule, the language used
in cryptograms exchanged between members of large organizations is the
mother tongue of the correspondents. Where this is not the case, that is,
when cryptograms of unknown origin must be studied, the cryptanalyst
looks for any indications on the cryptograms themselves which may lead to
a conclusion as to the language enployed. Address, signature, and other
data, if in plain text in the preamble, in the body, or at the end of the
cryptogram, all come under careful scrutiny, as well as all extraneous
circumstances connected with the manner j.r which the cryptograms were
obtained, the person on whom they were found, or the locale of their
origin and destination.
b. In special cases, or under special circumstances a clue to the
language employed is found in the nature and composition of the crypto-
graphic text itself. For example, if the letters K and W are entirely
absent or appear very rarely in messages, it may indicate that the lan-
guage is Spanish, for these letters are absent in the alphabet of that
language and are used only to spell foreign words or names . The presence
of accented letters or letters marked with special signs of one sort or
another, peculiar to certain languages, will sometimes indicate the lan-
guage used. The Japanese Morse telegraph alphabet and the Russian Morse
telegraph alphabet contain combinations of dots and dashes which are
peculiar to those alphabets and thus the interception of messages con-
taining these special Morse combinations at once indicates the language
involved. Finally, there are certain peculiarities of alphabetic lan-
guages which, in certain types of cryptograms, viz ., pure transposition,
give clues as to the language vised. For example, the frequent digraph CH,
in German, leads to the presence, in cryptograms of the type mentioned,
of many isolated C‘s and H’s; if this is noted, the cryptogram may be
assumed to be in German.
c. In some cases it is perfectly possible to perform certain steps
in cryptanalysis before the language of the cryptogram has been definitely
determined. Frequency studies, for example, may be made and analytic
processes performed without this knowledge, and by a cryptanalyst wholly
unfamiliar with the language even if it has been identified, or who knows
only enough about the language to enable him to recognize valid combina-
tions of letters, syllables, or a few common words in that language. He
may, after this, call to his assistance a translator who may not be a
cryptanalyst but who can materially aid in making necessary assumptions
based upon his special knowledge of the characteristics of the language
in question. Thus, cooperation between cryptanalyst and translator
results in solution. 2
2 ^
- The writer has seen in print statements that "during World War _I_. . . . decoded messages in Japanese
and Russian without knowing a word of either language.” The ext \t to which such statements are exaggerated
will soon become obvious to the student. Of course, there are occasional instances in which a mere clerk with
xiiuite limited experience may be able to "solve” a message in an extremely simple system in a language of which
he has no knowledge at all; but such a “solution” calls for nothing more arduous than the ability to Tccognizc
pronounceable combinations of vowels and consonants— an ability that hardly deserves to be rated as "cr;pt-
analytic” in any real sense. To say that it is possible to solve a cryptogram in a foreign language "without
knowing a word of that language” is not quite the same as to say that it is possible to do so with only a slight
knowledge of the language; and it may be stated without cavil that the better the cryptanalyst's knowledge of
the language, tho greater are the chances for his success and, in any case, the easier is his work.
- REDTIUCTED 24
REF ID: A5 68 95
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17. The determination of the general system . — a. Except in the case
of the more simple types of cryptograms, the step referred to as diagnosis,
that is, ascertaining the general system according to which a given cryp-
togram has "been produced is usually a difficult, if not the most difficult,
step in its solution. The reason for this is not hard to find.
> b. As will become _ apparent to the student as he proceeds with his
study7 in the final analysis, the solution of every cryptogram involving
a form of substitution depends upon its reduction to monoalphabetic terms,
if it is not .originally in those terms . This is true not only of ordinary
substitution ciphers, but also of combined substitution-transposition
ciphers, and of enciphered code. If the cryptogram must be reduced to
monoalphabetic terms, the manner of its accomplishment is usually indi-
cated by the cryptogram itself, by external or Internal phenomena which
become apparent to the cryptanalyst as he studies the cryptogram. If
this Is impossible, or too difficult, the cryptanalyst must, by one means
or another, discover how to accomplish this reduction, by bringing to
bear all the special or collateral information he can get from all the
sources at his command. If both these possibilities fall him, there is
little left but the long, tedious, and often fruitless process of elimi-
nation. In the case of transposition ciphers of the more complex type,
the discovery of the basic method is often simply a matter of long and
tedious elimination of possibilities. For cryptanalysis has unfortunately
not yet attained, and may Indeed never attain, the precision found today
in qualitative analysis in chemistry, for example, where the analytic
process 1 b absolutely clear-cut and exact in its dichotomy. A few words
in explanation of what is meant may not be amiss. When a chemist seeks
to determine the identity of an unknown substance, he applies certain
specific reagents to the substance and in a specific sequence. The first
reagent tells him definitely into which of two primary classes the unknown
substance falls. He then applies a second test with another specific
reagent, which tells him again quite definitely into which of two second-
ary classes the unknown substance falls, and so on, until finally he has
reduced the unknown substance to its simplest terms and has found out
what it is. In striking contrast to this situation, cryptanalysis affords
exceedingly few "reagents" or tests that may be applied to determine posi-
tively that a given cipher belongs to one or the ‘ other “of two systems
yielding externally similar results. And this is what makes the analysis
of. an isolated, complex cryptogram so difficult. Rote the limiting adjec-
tive "isolated" in the foregoing sentence, for it is used advisedly. It
is not often that the general system fails to disclose itself or cannot
be discovered by painstaking Investigation when there is a great volume
of text accumulating from a regular traffic between numerous corre-
spondents in a large organization. Sooner or later the system becomes
known, either because of blunders and carelessness on the part of the
personnel entrusted with the encrypting of the messages, or because the
accumulation of text itself makes possible the determination of the
general system by cryptanalytic, including statistical, studies. But in
25
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REF ID: A5 68 95
the ease of a single or even a few Isolated cryptograms concerning which
little or no information can he gained hy the cryptanalyst, he is often
unable, without a knowledge of, or a shrewd guess as to the general system
employed, to decompose the heterogeneous text of the cryptogram into
homogeneous, monoalphahetic text, which is 'rhe ultimate and essential
step in analysis . The only knowledge that the cryptanalyst can bring to
his aid in this most difficult step is that gained hy long experience and
practice in the analysis of many different types of systems. In this
respect the practice of cryptanalysis is analogous to the practice of
medicine: correct diagnosis is the most important and often the most
difficult first step toward success.
c. On account of the complexities surrounding this particular phase ■
of cryptanalysis, and because in any scheme of analysis based upon suc-
cessive eliminations of alternatives the cryptanalyst can only progress
as far as the extent of his own knowledge of all the possible alternatives
will permit, it is necessary that detailed discussion of the eliminative
process be postponed until the student has covered most of the field.
For example, the student will perhaps want to know 1 at once how he can
distinguish between a cryptogram that is in code or enciphered code from
one that is in cipher. It is at this stage of his studies impracticable
to give him any helpful indications on his question. In return it may be
asked of him why he should expect to be able to do this in the early
stages of his studies when often the experienced expert oryptanalyst is
baffled on the same score!
d. nevertheless, in lieu of more precise diagnostic tests not yet
discovered, a general guide that may be useful in cryptanalysis will be
built up, step by step as the student progresses, in the form of a series
of charts comprising what may be designated An Analytical Key for Crypt-
analysis . (See Section X.) It may be of assistance to the student if,
as he proceeds, he will carefully study the charts and note the place
which the particular cipher he is solving occupies in the general crypt -
analytic panorama. These charts admittedly constitute only very brief
outlines, and can therefore be of but little direct assistance to him
In the analysis of the more complex types of cryptosystems he may en-
counter later on. . So far as they go, however, they may be found to be
quite useful in the study of elementary cryptanalysis. For the expe-
rienced cryptanalyst they can serve only as a means of assuring that no
possible step or process is inadvertently overlooked in attempts to solve
a difficult cryptosystem.
e. Much of the labor Involved In crypt analytic work, as referred
to ln’par. 2, Is connected with this determination of the general system.
The preparation of the text, its rewriting in different forms, sometimes
being rewritten in dozens of ways, the recording of letters, the estab-
lishment of frequencies of occurrences of letters, comparisons and
experiments made with known material of similar character, and so on,
constitute much labor that is most often indispensable, but which
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2 6
REF ID: A5 68 95
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sometimes turns out to have "been wholly unnecessary, or 4n vain. In one
treatise^ it is stated quite "boldly that "this work, once done, the deter-
mination. of the system is often relatively easy," This statement can
certainly apply only to the simpler types of cryptosystems j it is entirely
misleading as regards the much more frequently encountered complex
cryptograms of modern times.
18, The reconstruction of the specific key .— a.- Nearly all practi-
cal cryptographic methods require the use of a specific key to guide,
control, or modify the various steps under the general system. Once the
latter has "been disclosed, discovered, or has otherwise come into the _ -
possession of the cryptanalyst, the next step in solution is to determine,
if necessary and if possible, the specific key that was employed to en-
crypt the message or messages tinder examination. This determination may
not "be in complete detail; it may go~ only so ’far as to lead to a know-
ledge of the number of alphabets involved in a substitution cipher, or
the number of columns involved in a transposition cipher, or that a one-
part code has been used, in the case of a code system. But It is often
desirable to determine the specific key in as complete a form and with
as much detail as possible, for this information will very frequently be
useful in the solution of subsequent cryptograms exchanged between the
same correspondents, since the nature or source of the specific key in a
solved case may be expected to give clues to the specific key in an
unsolved case.
b. Frequently, however, the reconstruction of the key is not a
prerequisite to, and does not constitute an absolutely necessary preli-
minary step in, the fourth basic operation, viz ., the reconstruction or
establishment of the plain text. In many cases, indeed, the two processes
are carried along simultaneously, the one assisting the other, until in
the final stages both have been completed in their entireties. In still
other .cases the reconstruction of the specific key may follow the recon-
struction of the plain 'text instead of preceding it and is accomplished
purely a3 a matter of academic interest; or the specific key may, in
unusual cases, never be reconstructed.
19. The reconstruction of the plain text .— a. Little need be said
at thifl point on this phase of cryptanalysis . The process usually con-
sists, in the case of substitution ciphers, in 'the establishment of
equivalency between specific letters of the cipher text and the plain
text, letter by letter, pair by pair, and so on, depending upon the par-
ticular type of substitution system involved. In the case of transposi-
tion ciphers, the process consists in rearranging the elements of the
cipher text, letter by letter, pair by pair, or occasionally word by
word, depending upon the particular type of transposition system involved,
until the letters or words have been returned to their original plaintext
order. In the case of code, the process consists in determining the
meaning of each code group and inserting this meaning in the code text to
reestablish the original plain text.
3 Lange et Soudart, op. cit., p. 10 6 .
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27
i * »
REF ID : A56895
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b. The foregoing processes do not, as a rule, begin at the begin-
ning of a message and continue letter by letter, or group by group in
sequence up to the very end of the message. The establishment of values
of cipher letters in substitution methods, or of the positions to which
cipher letters should be transferred to form the plain text in the case
of transposition methods, comes at very irregular intervals in the pro-
cess . At first only one or two values scattered here and there through-
out the text may appear; these then form the "skeletons" of words, upon
which further work, by a continuation of the reconstruction process, is
made possible; in the end the complete or nearly complete 11 ' text is
established.
c. In the case of cryptograms in a foreign language, the transla-
tion of the solved messages is a final and necessary step, but is not to
be considered as a cryptanalytic process. However, it is commonly the
case that the translation process will be carried on simultaneously with
the cryptanalytic, and will aid the latter, especially when there are
lacunae which may be filled in from the context. (See also subpar. l6c
in this connection.)
20. The utilization of traffic intercepts . 5 — a. There are, of
course, other operations which are not as basic in nature as those just
outlined but which must generally be performed as preliminary steps in
practical cryptanalytic work (as distinguished from academic cryptana-
lysis)"! Before a military cryptanalyst can begin the analysis of an
enemy cryptosystem, it is necessary for him to study the intercept mate-
rial that is available to him, isolate the messages that hve been
encrypted by means of the cryptosystem to be exploited, and to arrange
the latter in a systematic order for analysis . This work, although
apparently very simple, may require a great deal of time and effort.
b. Since, whenever practicable, two or more intercept stations
are assigned to copy traffic emanating from the stations of one enemy
radio net, it is natural that there should be a certain amount of
duplication in the work of the several stations. This is desirable
since it provides the cryptanalysts with two or more sets of the same
messages, so that when one intercept station fails to receive all the
messages completely and correctly, because of radio difficulties, local
static, or poor operation, it is possible by studying the other sets to
reconstruct accurately the entire traffic of the enemy net .
^ Sometimes in the case of code, the meaning of a small percentage
of the code groups occurring in the traffic may be lacking, because
there is insufficient text to establish their meaning.
5 A traffic intercept is a copy of a communication gained through
interception.
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28
REF ID: A56895
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c. In all intct'cepfc activities vhcre operators are used for copying
the traffic, one of the most likely errors to he found is caused by the
human element in reception. For this reason cryptanalysts and their
Chart 1. Most common errors in telegraphic transmission.
assistants should be familiar with the international Morse alphabet and
the most common errors in wire and radio transmission methods so as to be
able to correct garbled groups when they occur. In this connection,
Chart 1, above, will be found useful.
C
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29
REF ID: A5 68 95
REF ID: A5 68 95
" REGTRICTED -
SECTION IV
FREQUENCY DISTRIBUTIONS AND THEIR FUNDAMENTAL USES
Paragraph
The simple or uniliteral frequency distribution 21
Important features of the normal uniliteral frequency
distribution 22
Constancy of the standard or normal unlliteral frequency
distribution 23
The three facts which can be determined from a study of the
uniliteral frequency distribution for a cryptogram. ......... 24
Determining the class to which a cipher belongs 25
Determining whether a substitution cipher is monoalphabetic or
non-monoalphabet ic 2 6
The $ (phi) test for determining monoalphabeticity 2?
Determining whether a cipher alphabet is standard (direct
or reversed) or mixed ' 28
21. The simple or uniliteral frequency distribution . — «• It has
long been known to cryptographers and typographers +*>at the” letters com-
posing the words of any intelligible written text composed in any language
which is alphabetic in construction are employed with greatly varying
frequencies. For example, if on cross-section paper a simple tabulation,
shown in Fig. 1, called a unlliteral frequency distribution , is made of
the letters composing the words of the preceding sentence, the variation
in frequency is strikingly demonstrated. It is seen that whereas certain
letters, such as A, E, I, N, 0, R, and T, are employed very frequently,
other letters, such as C, G, H, L, P, and S are employed not nearly so
frequently, while still other letters, such as F, J, K, Q, V, X, and Z
are employed either seldom or not at all.
* g
. 3^
ABCDEFGHIJKLMNOPQRSTUVWXYZ
14 3 8 4 22 2 9 10 15 0 1 9 3 17 14 8 1 13 10 20 3 J 0 1 7 0
(Total=200 letters)
Figure 1.
h. If a similar tabulation .is now made of the letters comprising the
words of the second sentence In the preceding subparagraph, the distribu-
tion shown in Fig. 2 is obtained. Both sentences have exactly the same
number of letters (200) .
31
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REF ID: A 5 68 95
g 5%?^ g § II. gll
Iglllllll >I|III= 5 |||?.^S
ABCDEFGHIJKLMNOPQRSTUVWXYZ
12 2 8 7267 4 6200 1 9 5 17 14 0 2 13 14 17 0 1 3 1 3 0
(Total=200 letter*}
Figure 2 .
c. Although each of these two distributions exhibits great varia-
tion In the relative frequencies with which different letters are employed
in the respective sentences to’ which they apply, no marked differences
are exhibited between the frequencies of the same letter in the two dis-
tributions* Compare, for example, the frequencies of A, B, C • • • Z in
Fig. 1 with those of A, B, C . . . Z in Fig. 2 . Aside from one or two
exceptions, as in the case of the letter F, these two distributions agree
rather strikingly.
•>
d. This agreement, or similarity , would be practically complete if
the two texts were much longer, for example, five times as long. In fact,
when two texts of similar character, each containing more than 1,000 let-
ters, are compared, it would be found that the respective frequencies of
the 26 letters composing the two distributions show only very slight dlf- •
ferences. This means, in other words, that in normal plain text each
letter of the alphabet occurs with a rather constant or characteristic
frequency which it tends to approximate, depending upon the length of the
text analyzed. The longer the text (within certain limits), the closer
will be the approximation to the characteristic frequencies of letters
in the language involved. However, when the amount of text being ana-
lyzed has reached a substantial volume (roughly, 1,000 letters), the prac-
tical gain in accuracy does not warrant further increase in the amount
of texb.- 1 -
e. An experiment along these lines will be convincing. A series
of 265 official telegrams 2 passing through the Department of the Army
Message Center was examined statistically.' The messages were divided
into five sets, each totaling 10,000 letters, and the five distributions
shown in Table 1 -A, were obtained.
1 See footnote 5 , page 38.
2 These comprised messages from several official sources in addition
to the Department of the Army and were all of an administrative character.
•nTrmrnmnriTnn
3 2
REF ID : A56895
Table 1-A. — Absolute frequencies of letters appearing in five sets of Governmental plain-text
each set containing 10,000 letters, arranged alphabetically
Absolute
Frequency
738
104
819
887
1,367
253
166
310
742
18
36
365
242
786
685
241
40
760
658
936
270
163
166
43
191
14
TotaL 10,000
Absolute
Frequency
788
103
800
413
1,294
287
176
351
750
17
38
393
240
794
770
272
22
746
583
879
233
173
163
60
155
17
10,000
Absolute
Frequency
Absolute
Frequency
740
83
826
451
1,270
287
167
3‘49
700
21
21
386
249
800
756
245
38
785
628
958
247
183
183
58
213
11
10,000
Absolute
Frequency
f . If the five distributions in Table 1-A are summed, the results
are as shown in Table 2-A« - .... \
Table 2-A. — Absolute frequencies
ides of letters appearing in the combined five sets of messages totaling
60,000 letters, arranged alphabetically
A... .
3, 683
6
819
L.
1 ,821
0- —
175
V.
766
B.
487
H
1,694
M.
1 ,237
R.
3, 788
w.
780
C
1,534
I„...
3,676
N„ ..
3 ,975
S.
3, 058
X.
231
D.
2, 122
J._.
82
0
3 ,764
T.
4,595
y.
967
E. .. .
F.
6,498
1,416
K
248
P.
1 ,335
U.
1,300
- - 1
z.
49
33
REF ID: A5 68 95
g. The frequencies noted in Table 2-A above, when reduced to the
basis of 1,000 letters and then used as a basis for constructing a simple
chart that will exhibit the variations in frequency in a striking manner,
yield the following distribution which is hereafter designated as the
normal or standard uniliteral frequency distribution for English
telegraphic plain text:
ABC
g g g
D E F
74 10 31 43 130 28
g g g g
g g g g
g g g g
g - g g g
g g g g
g g g g
g g g g g g
gg gggg _ §
gg gggggg Ig
gg gggggg g
ggssgggggggg-.
OPflRSTUVWXtZ
75 37 3 78 01 02 20 14 10 S IS 1
Figure 3.
22. Important features of the normal uniliteral frequency distri -
bution .'— a. When the distribution shown in Fig. 3 is studied in detail,
the following features are apparent:
(1) It is quite irregular in appearance. This is because the letters
are used with greatly varying frequencies, as discussed in the preceding
paragraph. This irregular appearance is often described by saying that
the distribution shows marked crests and troughs , that is, points of high
frequency and low frequency.
(2) The relative positions in which the crests and troughs fall
within the distribution, that is, the spatial relations of the crests and
troughs, are rather definitely fixed and are determined by circumstances
which have been explained in subpar. 13 b.
(3) The relative heights and depths of the crests and troughs within
the distribution, that is, the linear extensions of the lines marking the
respective frequencies, sre also rather definitely fixed, as would be
found if an equal volume of similar text were analyzed.
34
REF ID: A5 68 95
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00 The most prominent crests are marked by the vowels A, E, I, 0,
and. the consonants N, R, S, Tj the most prominent troughs are marked by
the consonants .J, K, Q, X, and Z.
(5) The important data are summarized in tabular form in Table 3*
- ' T _ «
Table 3
1 ^ _ _
l
Frequency
Percent of
total
Percent of
total in
round
numbers
6 Vowels: A E X 0 U Y.‘ .1
398
39.8
40
20 Conson&nts:
5 High Frequency (D HRS T)
350
35.0
35
10 Medium Frequency (BCFGHLMPV W)
238
23.8
24
5 Low Frequency ( J K Q X Z)
14
1.4
!
1
Total . . -- . _ „ _ _ - _
1,000
100. 0
100
(6) The frequencies of the letters of the alphabet, reduced to a
"base of
1000, are
as
follows: ■
A. ..
74
G
Ifi
T.
36 Q-.
3
v„
Ifi
B
„ 10
H_„.
34.
M
25 R..
7fi
ff-
16
c
31
I_
74
to
79 S„
fil
X.
fi
D
42
J__
2
0
75 T..
_ Q2
Y_
IQ
E. ..
130
K
3
p
27 U-.
2fi
1
F
28
(7)
The relative
order of
frequency of the
letters Is
as
follows :
' E
. . 130
i_
74
C._
31 Y.
19
X..
k
T
92
s...
61
F
28 G.
" ' 1 ft
3
N
79
D...
42
R
27 W.
_ _____ ifi
K,.
3
R
76
L„.
36
U
26 V.
15
J..
2
0
75
H_„
34
n
25 B.
10
ZL
1
A 74
(8) The four vowels A, E, I, 0 (combined frequency 353) and the foul*
consonants N, R, S, T (combined frequency 308) form 66l out of every
1,000 letters of plain text; in other words, less than one-third of the
alphabet is employed in writing two-thirds of normal plain text.
d. As a matter of fact, other tables compiled from Army sources
gave Slightly different results, depending upon the source of the text.
For example, three tables based upon 75,000, 100,000, and 136,257 letters
taken from various sources (telegrams, newspapers, magazine articles,
books of fiction) gave as the relative order of frequency for the first
10 letters the following:
For 75,000 letters ETRNIOASDL
For 100,000 letters ETRIUOASDL
For 136,257 letters ETRNAOISLD
3 Just as the individual letters constituting a large volume of plain
text have more or less characteristic or fixed frequencies, so it is
found that d igraphs and trigraphs (two- and three -letter combinations,
respectively)" have characteristic frequencies, when a large volume of
text is studied statistically. In Table 6 of Appendix 2, "Letter fre-
quency data - English", are shercm the relative frequencies of all digraphs
appearing in the 260 telegrams referred to in subpar. 21e. This appendix
also includes several other kinds of tables and lists of frequency data
which ■trill be useful to the student in his work. It is suggested that
the student refer to this appendix now, to gain an idea of the data
available for his future reference.
Other languages, of course, each have their own individual charac-
teristic plaintext frequencies of single letters, digraphs, trigraphs,
etc . A brief su'iutiary of the letter frequency data for German, French,
I-: 'Vilen, Spanish, Portuguese, and Russian constitute Appendix 5, "Letter
f* jqucncy data - foreign languages".
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• 1 ^
N
b. The data given in Fig. 3 and Table 3 represent the relati^ fre-
quencies found in a large volume of English telegraphic text of a govern-
mental, administrative character .3 These frequencies will vary somewhat
with the nature of the text analyzed. - For' example, if an equal number
of telegrams dealing solely with commercial transactions in the leather
industry were studied statistically, the frequencies would be slightly
different because of the repeated occurrence of words peculiar to that
industry. Again, if an equal number of telegrams dealing solely with
military messages of a tactical character were studied statistically,
the frequencies would differ slightly from those found above for geberal
governmental messages of .an administrative character. f
t .
c . If ordinary English literary text (such as may be found in any
book, "newspaper, or printed document) were analyzed, the frequencies of
certain letters would be changed to an appreciable degree. This is
because in telegraphic text words which are not strictly essential for
intelligibility (such as the definite and indefinite articles, certain
prepositions, conjunctions , and pronouns) are omitted. In addition,
certain essential words, such as "stop", "period", "comma", and the like,
which are usually indicated in written or printed matter by symbols not
easy to transmit telegraphically and which must, therefore, be spelled
out in telegrams, occur very frequently. Furthermore , telegraphic text
often employs longer and more uncommon words than does ordinary newspaper
or hook texb.
36
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REF ID: A5 68 95
e. Frequency data applicable purely to English military text were
compiled by Hitt/ 1- from a study of 10,000 letters taken from orders and
reports. The frequencies found by him are given in Tables k and 5.
Table 4. — Frequency table jor 10,000 letters of literary English, as compiled by Hitt
ALPHABETICALLY ARRANGED
A.
778
G...
174
L.
372
q *
vl.
112
B.
141
H__.
595
M
288
R 651
w.
176
C. ...
296
I...
667
N
686
S. 622
X
27
D.
402
J._
51
0.
807
T. 855
Y„
196
E.
1 ,277
K...
74
P.
223
u ana
z.
17
F.
197
ARRANGED
ACCORDING TO
FREQUENCY
E
l ,277
R...
651
11
308
Y 196
K
74
T.
855
S...
622
c
296
W . 176
J
51
0
807
H__
595
M ...
288
G. 174
X.
27
A
778
D...
402
P.
223
B ...... 141
z.
17
N.
686
L...
372
F.
197
V. 112
Q.
8
I
667
Table 5. — Frequency table jor 10,000 letters of telegraphic English, as compiled by Hitt
ALPHABETICALLY ARRANGED
A
813
G..
201
L.
... 392
Q.
38
V.
136
B
149
H._
38fi
M
... 273
R
G77
ff
166
c
306
I..
711
N
... 718
s
656
X.
51
D.
417
J-.
42
0
... 844
T
634
Y
208
E......
1 ,319
K..
88
P.
... 243
u
321
z.
6
F
205
ARRANGED
ACCORDING TO
FREQUENCY
E
1 ,319
S_.
656
U.
... 321
F.
205
K_
88
0
844
T._
634
C___. .
... 306
G
201
X.
51
A.
813
D..
417
M
... 273
w.
166
J
42
N.
718
L..
392
P.
... 243
B
149
Q.
38
I.
711
HL.
386
Y.
... 208
V.
136
Z.
6
R.
677
23. Constancy of the standard or normal uniliteral frequency dis -
tribution . — a. The relative frequencies disclosed by the statistical
study of large volumes of text may be considered to be the standard or
normal frequencies of the letters of written English. Counts made, of
smaller volumes of text will Lend to approximate these normal frequencies,
1 0 p» cit ., pp. 6 - 7 .
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37
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A
and, vitliin certain limits, 5 the smaller the volume, the lower wilifbe
the degree of approximation to the normal, until, in the case of a ’• fery
short message, the normal proportions may not manifest themselves a-; all.
It is advisable that the student fix this fact firmly in mind, for ; ;he
sooner he realizes the true nature of any data relative to the frequency
of occurrence of letters in text, the less often will his labors toward
the solution of specific ciphers be thwarted and retarded by too strict
an adherence to these generalized principles of frequency. He should
constantly bear in mind that such data are merely statistical generaliza-
tions , that they will be found to hold strictly true only in large Volumes
of text, and that they may not pven be approximated in short messages.
b. Nevertheless the normal frequency distribution or the "normal
expectation" for any alphabetic language is, in the last analysis, the
best guide to, and the usual basis for, the solution of cryptograms of a
certain type. It is useful, therefore, to reduce the normal, uniliteral
frequency distribution to a basis that more or less closely approximates
the volume of text which the cryptanalyst most often encounters in indi-
vidual cryptograms. As regards length of messages, counting only the
letters in the body, and excluding address ahd signature, a study of
the 260 telegrams referred to in par. 21 shows that the arithmetical
average is 217 letters; the statistical mean, or weighted average®,
however, is 191 letters. These two results are, however, close enough
together to warrant the statement that the average length of telegrams is
approximately 200 letters. The frequencies given in par. 21 have there-
fore been reduced to a basis of 200 letters, and the following unilite-
ral frequency distribution may be taken as showing the most typical
distribution to be expected in 200 letters of English telegraphic text:
.
g - ^
g g g I g g 5 = 3
g =* g is g g ggg
g g g g g S: g g
ABCDEFGHIJKLMfcOPQRSTUVWXYZ
Figure 4.
?It is useless to go beyond a certain limit in establishing the nofmal-frequency distribution for & given
language. As a striking instance of this fact, witness the frequenoy study made by an indefatigable German,
Kacding, who in 1898 made a count Of the letters in about 11,0(10,000' words, totaling about 62,000,000 tetters in
German text. When reduced to a percentage basis, and when the relative order of frequency was determined,
the results he obtained differed very little from the results obtained by Kasiairi, a German cryptographer, from a
count of only 1,000 letters. See Kaeding, Itdeufigkeilsiooet-lerbuch, Steglitz, 1898; jfcaslsld, I)ie Qeheimschriften
und die Dechijfrir-Kunst, Berlin, 1863.
/ I
0 The arithmetical average is obtained by adding each different length
and dividing by the number of different -length messages; the mean is ob-
tained by multiplying each different length by the number of messages of
that length, adding all products , ahd dividing hy the tptal number of
messages .
38
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c. The student should take careful note of the appearance of the
distribution? shown in Fig. *1, for it will he of much assistance to him
in the early stages of his study. The manner of setting down the tallies
should he followed hy him in making his own distributions, indicating
every fifth occurrence of a letter hy an oblique tally. This procedure
almost automatically shows the total number of occurrences for each let-
ter, and yet does not destroy the graphical appearance of the distribu-
tion, especially if care is taken to use approximately the same amount
of space for each set of five tallies. Cross-section paper is very
useful for this purpose.
d, The word "uniliteral" in the designation "uniliteral frequency
distribution" means "single letter", and it is to he inferred that other
types of frequency distributions may he encountered. For example, a
distribution of pairs of letters , constituting a hiliteral frequency
distribution, is very often used in the study of certain cryptograms in
which it is desired that pairs made hy combining successive letters he
listed. A hiliteral distribution of A B C D E F would take these pairs:
AB, BC, CD, DE, EF. The distribution could he made in the form of a
large square divided up into 676 cells . When distributions beyond hi-
literal are required (triliteral, quadriliteral, etc.) they can only he
made hy listing them in some order, for example, alphabetically based on
the 1st, 2d, 3d, . . . letter.
? The use of the terms "distribution" and "frequency distribution",
instead of "table" and "frequency table", respectively, is considered
advisable from the point of view of consistency with the usual statistical
nomenclature. When data are given in tabular form, with frequencies
indicated hy numbers , then they may properly he said to he set out in
the form of a table . When, however, the same data are distributed in a
chart which partakes of the nature of a graph, with the data indicated
hy horizontal or vertical linear extensions, or hy a curve connecting
points corresponding to quantities, then it is more proper to call such
a graphic representation of the data a distribution .
J.VUU JL X JUI^ * -c
i
24. The three facts wMefa can 'be determined from a study of the
unllitoral frcqiiency distribution for a cryptogram . -"-a. The following
three facts (to he explained subsequently) can usually he determined from
an inspection of the uniliteral frequency distribution for a given cipher
message of average length, composed of letters:
(1) Whether the cipher belongs to the substitution or the transpo-
sition class; 4
(2) If to the former, whether it ir monoalphabetic® or non-
monoalphabet ic 9 in character;
•i
(3) If monoalphabet ic, whether the cipher alphabet is standard
(direct or reversed) or mixed. *
b. For immediate purposes the first two of the foregoing determi-
nations are quite important and will be discussed in detail in the next
two paragraphs ; the other determination will be touched upon very briefly,
leaving its detailed discussion for subsequent sections of the text#
2$, Determining the class to which a cipher belong s,— a# The deter-
mination of the class to which a cipher belongs is usually a relatively
easy matter because of the fundamental difference between transposition
and substitution as cryptographic processes# In a transposition cipher
the original letters of the plain text have merely been rearranged,
vithout any change whatsoever in their identities, that is, in the
conventional values they have in the normal alphabet. Hence, the nurfbers
of vowels (A, E, I, 0, U, Y), high-frequency consonants (D, N, R, S, T),
me&iun-f re queney consonants (B, C, F, G, H, L, M, P, V, W), and low-
frcquency consonants (J, K, Q, X, Z) are exactly the same in the
cryptogram as they are in the plaintext message. Therefore, the
percentages of vowels, high-, medium-, and low-frequency consonants are
the some in the transposed text as in the equivalent plain text. In a
& In connection with uniliteral frequency distributions, the term
mono alphabetic is considered to embrace the concept of monoalphabetic-
monographic -uniliteral systems only, thus excluding polygraphic and
multilitoral systems, both of which, however, usually fall into the
mouoalphabetic category.
9 The term non-monoalphabetic as applied in this instance IS consi-
dered to embrace all deviations from the characteristic appearance of
monoalphabetic distributions* These deviations include the phenomena
inherent in polyalphabetic, polygraphic, and multiliteral cryptograms,
as well as in random text, i.c., text which appears to have been pro-
duced by chance or accident, having no discernible patterns or
limitations .
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substitution cipher, on the other hand, tho identities of the original
.letters of the plsin_ text have hcen •changed, that is, the conventional
values they have in tli'e’ normal alphabet have been altered. Consequently,
if a count is made of the various letters present "in such a cryptogram,
it will he found that tho number of vowels, high-, medium-, and low-
frequency consonants will usually he quite different in tho cryptogram
from what they are in the original plaintext message. Therefore, the
percentages of vowels, high-’, medium-, and low-fr'e quency consonants are
usually quite different in the substitution text from what they ere in
the equivalent plain text. Prom these considerations it .follows that if
in a specific cryptogram the percentages of vowels, high-, medium-, and
low-frequcncy consonants are approximately the same as vould be expected
in normal plain text, the cryptogram probably belongs to the transposition
class; if these percentages are quite different from those to be expected
in normal plain text the cryptogram probably belongs to the substitution
class .
b. In the preceding subparagraph the word ’'probably was emphasized
by italicizing it, for there can be no certainty in every case of this
determination. Usually these percentages in a transposition cipher are
close to the normal percentages for plain text; usually , in a substitu-
tion cipher, they are far different from the normal percentages for plain
text. But occasionally a cipher message is encountered which is difficult
to classify with a reasonable degree of certainty because the message is
too short for the general principles of frequency to manifest themselves.
It is clear that if in actual messages there were no variation whatever
from the normal vowel and consonant percentages given in Table 3, the
aexerraination of the class to which a specific cryptogram belongs would
be an extremely simple matter. But unfortunately there is always some
variation or deviation from the normal.. Intuition suggests that as
messages decrease in length there may be a greater and greater departure
from the normal proportions of vowels , high-, medium-, and low-frequency
consonants, until in very short messages the normal proportions may not
hold at all. Similarly, as messages increase in length there may be a
lesser and lesser departure from the normal proportions, until in messages
totalling a thousand or more letters there may be no difference at all
between the actual and the theoretical proportions. But Intuition is not
enough, for in dealing vith specific messages of the length of those
commonly encountered in practical work the question sometimes arises as
to exactly hour much deviation (from the normal proportions) may be allowed
for in a cryptogram which shows a considerable amount of deviation from
the normal and which might still belong to the transposition rather than
to the substitution class.
£. Statistical studies have been made on this matter and some graphs
have been constructed thereon. These are shewn in Charts 2 - 5 in the
form of simple curves, the use of which will now be explained. Each
chart contains two curves marking the lower and upper limits, respect-
ively, of the theoretical amount of deviation (from the normal percent -
) of vowels or consonants which may be allowable in a cipher believed
to belong to the transposition class.
la'
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d. In Chart 2, curve V]_ marks the lower limit of the theoretical
amount of deviation 1 *-* from the number of vowels theoretically expected to
appear 11 in a message of given length} curve Vg marks the upper limit
of the same statistic. Thus, for example, in a message of 100 letters
in plain English there should he between 33 and 47 vowels (A E I 0 U Y) •
Likewise, in Chart 3 curves Hq and H2 mark the lower and upper limits as
regards the high-frequency consonants. In a message of 100 letters jthere
should he between 28 and 42 high-frequency consonants (DURST), .In
Chart 4 curves Mi and M2 mark the lower and upper limits as regards ithe
medium-frequency consonants . In a message of 100 letters there should he
between 17 and 31 medium- frequency, consonants (BCFGHLMPVW).
Finally, in Chart 5# curves Li and L2 mark the lower and upper limits as
regards the low-frequency consonants . In a message of 100 letters there
should he between 0 and 3 low-frequency consonants (J K Q X J5) « In using
the charts, therefore, one finds the point of intersection of the vertical
coordinate corresponding to the length of the message, with the horizontal
coordinate corresponding to (l) the number of vowels, (2) the number
of high-frequency consonants, (3) the number of medium-frequency con-
sonants, and* (4) the number of low-frequency consonants actually counted
in the message. If all four points of intersection fall within the
area delimited by the respective curves, then the numbers of vowels and
high-, medium-, and low-frequency consonants correspond with the numbers
theoretically expected iii a 'normal plaintext message of the same length}
since the message under investigation is not plain text, it follows that
the cryptogram may certainly be classified as a transposition aipher. On
the other hand, if one or more of these points of intersection fall out-
side the area delimited by the respective curves, it follows that the
cryptogram Is probably a substitution cipher. The distance that the point
of intersection falls outside the area delimited by these curves is a more
or less rough measure of the improbability of the cryptogram's being a
transposition cipher.
e. Sometimes a cryptogram is encountered which is hard to classify
with "certainty even with the foregoing aids, because it has been con-
sciously prepared with a view to making the classification difficult.
This can be done either by selecting peculiar words (as in “trick crypto-
grams") or by employing a cipher alphabet in which letters of approx -
imately similar normal frequencies have been interchanged. For example,
E may be replaced by 0, T by R, and so on, thus yielding a cryptogram
giving external indications of being a transposition cipher but which is
really a substitution cipher. If the cryptogram is not too short, a close
study -trill usually disclose what has been done, as well as the futility of
so simple a subterfuge ,
10 In Charts 2-5, inclusive, the limits of the upper and lower curves
have been calculated to include approximately 70 percent of messages of
the various lengths.
11 The expression “the number of ... theoretically expected to appear"
is often condensed to "the theoretical expectation of ..." or "the normal
expectation of
10 20 30 40 £0 60 70 80 90 100 1 10 120 130 140 150 160 170 180 190 200
Number of letters in mossago.
Chart 2. Curves marking the lower and upper limits of
the theoretical amount of deviation from the number of vowels
theoretically expected in messages of various lengths.
(See subpax. 25d.)
tion ciphers. In the former case, his eyes very speedily note many high-
frequency letters, such as E, T, N, R, 0, and S, with the absence of
loir-frequency letters, such as J, K, Q, X, and Z; in the latter case, his
eyes just as quickly note the presence of many low-frequency letters, and
a corresponding absence of some of the high-frequency letters .
I
43
REF ID : A56895
£. Another rather quickly completed test, in the case of the simpler
varieties of ciphers, is to look for repetitions of groups of letters * As
will become apparent very soon, recurrences of syllables, entire wbrds and
short phrases constitute a characteristic of all normal plain text!. Since
a transposition cipher involves a change i r the sequence of the letters
■■■■■■■■■■■■■■■I
siii
10 20 30 40 50 60 70 80 90 1
IfO 120 I
160 170 I
Number of letters in message.
Chart 3* Curves marking the lower and upper limits of
the theoretical amount of deviation from the nuniber of high-
frequency consonants theoretically expected in messages of
various lengths. (See subpar . 25d.)
composing a plaintext message, such recurrences are broken up so that
the cipher text no longer will show repetitions of more or less lengthy
sequences of letters. But if a cipher message does show many repetitions
and these are of several letters in length, say over four or five, the
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conclusion is at once warranted that the cryptogram Is most probably a
substitution and not a tranposition cipher. However, for the beginner
in cryptanalysis, it will be advisable to make the uniliteral frequency
distribution, and note the frequencies of the vowels and of the high-,
Number of letters in message.
Chart 4. Curves marking the lower and upper limits of
the theoretical amount of deviation from the number of medium-
frequency consonants theoretically expected in messages of
various lengths. (See subpar. 25d.)
t
medium-, and low-frequency consonants. Then, referring to Charts 2 to 5,
he should carefully note whether or not the observed frequencies for these
categories of letters fall within the limits of the theoretical frequen-
cies for a normal plaintext message of the same length, and be guided
accordingly.
45
REF ID : A56895
- II
h. It is obvious that the foregoing rule applies only to ciders
composted wholly of lettei's . If a message is composed entirely of! figures,
or of arbitrary signs and symbols, or of intermixtures of letters j • figures
and other symbols, it is immediately apparent that the cryptogram -is a
substitution cipher. -j
Number of Iottors in mossago.
Chart 5 • Curves marking the lower and upper limits of
the theoretical amount of deviation from the nuaiber of low-
frequency consonants theoretically expected in messages of
various lengths. (See subpar. 25d„)
jL. Finally, It should be mentioned that there are certain kipds of
cryptograms whose class cannot be determined by the method set forth Jr
subparagraph d above . These exceptions will be discussed in a subsequent
section of this text.^
12 Section X.
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2 6 . Determining whether a substitution cipher 1b monoalphabetlc or
non-roonoalphabetic . — a . It will be remembered that a monoalphabetlc
substitution cipher is one in which a single cipher alphabet is employed
throughout the whole message; that is, a given plaintext letter is in-
variably represented throughout the message by one and the same letter in
the cipher text* On the other hand, a polyalphabetic substitution cipher
is one in which two or more cipher alphabets are employed within the same
message; that is, a given plaintext letter may be represented by two or
more different letters in the cipher text, according to some rule govern-
ing the selection of the equivalent to be used In each case. From this
it follows that a single cipher letter may represent two or more different
plaintext letters. A similar situation prevails in the case of multi -
literal substitution, in which a particular cipher letter may constitute
a part of 'the equivalents for several plaintext letters, giving rise to
phenomena resembling those of polyalphabeticity.
b. It is easy to see why and how the appearance of the uniliteral
frequency distribution for a substitution cipher may be used to determine
whether the cryptogram is monoalphabetlc or non-monoalphabetic in char-
acter. The normal distribution presents marked crests and troughs by
virtue of two circumstances. First, the elementary sounds which the
symbols represent are used with greatly varying frequencies, it being one
of the striking characteristics of every alphabetic language that its
elementary sounds are used with greatly varying frequencies .33 In the
second place, except for orthographic aberrations peculiar to certain
languages (conspicuously, English and French) , each such sound Is rep-
resented by the same symbol. It follows, therefore, chat since in a
monoalphabetlc substitution cipher each different plaintext letter
(selementary sound) is represented by one and only one cipher letter
(^elementary symbol), the uniliteral frequency distribution for such a
cipher message must also exhibit the irregular crest-and-trough appearance
of the normal distribution, but with this important modification — the
absolute positions of the crests and troughs will not be the same as In
the normal . That is, the letters accompanying the crests and the troughs
in the distribution for the cryptogram will be different from those accom-
panying the crests and the troughs in the normal distribution. But the
marked irregularity or "roughness" of the distribution, that is, the
presence of accentuated crests and troughs, is in itself an indication
that each symbol or cipher letter always represents the same plaintext
letter in that cryptogram. Hence the general rule: A marked crest-and -
trough appearance in the unillteral frequency distribution for a given
cryptogram indicates that a single cipher alphabet is involved and
constitutes one of the tests for a monoalphabetlc substitution cipher .
c. On the other hand, suppose that in a cryptogram each cipher
letter represents several different plaintext letters. Some of them are
of high frequency, others of low frequency. The net result of such a
3-3 The student who is interested in this phase of the subject may find
the following reference of value: Zipf G.K., Selected Studies of the
Principle of Relative Frequency in Language , Cambridge, Mass . , 1932.
!
47
situation, so far as the uniliteral frequency distribution for th^ (
cryptogram is concerned, is to prevent the appearance of any markejl
crests and troughs and to tend to reduce the elements of the distribution
to a more or less common level. This imparts a "flattened out" appear-
ance to the distribution. For example, in a certain cryptogram of’
polyalphabetic construction, K c =E p , Cm, and J p ; RcsAp, Dp, and B p jl
Xc=Op, Lp, and F p . The frequencies of Kc, R c , and X c will be approx-
imately equal because the summations of the frequencies of the several
plaintext letters each of these cipher letters represents at different
times will be about equal. If this same phenomenon were true of all the
letters of the cryptogram, it is clear that the frequencies of th^ 2 6
letters , when shown by means of the ordinary uniliteral frequency dist-
ribution, would shew no striking differences and the distribution would
have the flat appearance of a typical polyalphabetic substitution cipher.
Hence, the general rules The absence of marked crests and troughs in the
unlliteral frequency distribution indicates that a c
itution is involved. The flattened-out appearance of the distribution
then, is one of the criteria for the rejection of a hypothesis of mono
alphabetic^ substitution .
d. The foregoing test based upon the appearance of the frequency
distribution is only one of several means of determing whether a sub-
stitution cipher is monoalphabetlc o.' non-monoalphabetic in composition.
It can be employed in cases yielding frequency distributions from which
definite conclusions can be drawn with more or less certainty by mere
ocular examination. In those cases in which the frequency distributions
contain insufficient data to permit drawing definite conclusions by such
examination, certain statistical tests can be applied. One of these
tests, called the <f> (phi) test, warrants detailed treatment and is
discussed in paragraph 27 below.
e* At this point, however, one additional test will be given be-
cause of its simplicity of application. This tesl, the A (lambda) or
blank-expectation test , may be employed in testing messages up to 200
letters in length, it being assumed that in messages of greater length
ocular examination of the frequency distribution offers little or no
difficulty. This test concerns the number of blanks in the frequency
distribution, that is, the number of letters of the alphabet which are
entirely absent from the message. It has been found from statistical
studies that rather definite "laws" govern the theoretically expected
number of blanks in normal plaintext messages and in frequency distribu-
tions for cryptograms of different natures and of various sizes . The
results of certain of these studies have been embodied in Chart 6.
ft This chart contains two curves . The one' labeled F applies to the
average number of blanks theoretically expected in frequency distributions
based upon normal plaintext messages of the indicated lengths. The other
curve, labeled R, applies to the average number of blanks theoretically
expected in frequency distributions based upon perfectly random assort-
ments of letters; that is, assortments such as would be found by random
Cf., footnote 8 on page 40.
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selection of letters out of a hat containing thousands of letters, all of
the 2 6 letters of the alphabet being present in equal proportions, each
letter being replaced after a record of its selection has been made. Such
random assortments correspond to polyalphabetic cipher messages in which
the number of cipher alphabets is so large that if unilateral frequency
distributions are made of the letters, the distributions are practically
identical with those vhich are obtained by random selections of letters
cut of a hat.
Chart 6. Curves showing the average number of blanks
theoretically expected in distributions for plain text (P)
and for random text (R) for messages of various lengths.
(See subpar . 26f.)
. g. In using this chart, one finds the point of intersection of the
vertical coordinate corresponding to the length of the message, with the
horizontal coordinate corresponding to the observed number of blanks in
the distribution for the message. If this point of intersection falls
closer to curve P than it does to curve R, the number of blanks in the
message approximates or corresponds more” closely to the number theoreti-
cally expected in a plaintext message than it does to a random (ciphertext)
message of the same length; therefore, this is evidence that the crypto-
- gram is monoalphabet ic . Conversely, if this point of intersection falls
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REF ID: A5 68 95
closer to curve R than to curve P, the number of blanks in the message ap-
proximates or corresponds more closely to the number theoretically expected
in a random text than it does to a plaintext message of the same length;
therefore, this is evidence that the cryptogram is non-monoalphabet ic •
I
27 . The j> (phi) test for determining monoalphabet ic lty « — a « 'i?he
student has seen in the preceding paragraph how it is possible” to deter-
mine by ocular examination whether or not a substitution cipher is i mono-
alphabetic. This tentative determination is based on the presence of a
marked crest-and-trough appearance in the unlliteral frequency distribu-
tion, and also on the number of blanks in the distribution* However, when
the distribution contains a small nuafber of elements, ocular examination
and evaluation becomes Increasingly difficult and uncertain. In such
cases, recourse may be had to a mathematical test, known as the <{> test,
to determine the relative monoalphabeticity or non-monoalphabetlclty of
a distribution*
b. Without going into the theory of probability at this time, or
into the derivation of the formulas involved, let it suffice for the pre-
sent to state that with this test the "observed value of <j>" (symbolized
"by 4>o) is compared with the "expected value of <j> random" (<)> r ) and the
"expected value of <j> plain" (<£ p) . The formulas are <J> r s.0385N(W-l) and,
for English military text, <j>ps.0667N(N-l), where H is the total number of
elements in the distribution. 15 The use of these formulas is best illus-
trated by an example .
c. The following short cryptogram with its accompanying uniliteral
frequency distribution is at hand:
QCYCH ADSKS Y Z Z Q E CYKYK QZYSK
LSZAC TKFCX LKLKC ESZMX KISZX
= b*£ N=50
ABCDEFGHIJKLMNOPQRSTUVWXYZ
15 The constant .0385 is the decimal equivalent of 1/26, i.e., the
reciprocal of the number of elements in the alphabet. The constant .0667
is the sum of the squares of the probabilities of occurrence of the indi-
vidual letters in English plain text. These constants are treated in
detail in Military Cryptanalysis, Part II.
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50
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<f>o is calculated by applying the formula f(f-l) to the frequency (f) of
each letter and totaling the result; or, expressed in mathematical
notation, 1 ® <j> 0 = if (f-l) • Thus,
£f = 2 6121 11 831 3 6l 356 = 50
ABCDEFGHIJKLMNQPQRSTUVWXYZ
Cf(f-l) : 2 30 020 00 5660 6 30 0 6 2030a 188
For this distribution, <j>r= *0385N(N-l)s.0385 x 50 x 49 = 94, and
<j>pr .0667W(N-l)s.0667 x 50 x 49 = 163.
How since c{> 0 , 186, is In fact greater than <tp, we have a mathematical
corroboration of the hypothesis that the cryptogram Is a monoalphabetic
substitution cipher* If <j> 0 were nearer to <! > r , then the assumption would
be that the cryptogram is not a monoalphabetic cipher* If <t> 0 were just
half way between <j> r and <j>p, then decision would have to be suspended,
since no further statistical proof in the matter is possible with this
particular test* 1 ”?
d. | Two further examples may be illustrated:
s _ = ^=25
(l) ABCDEFGHIJKLMNOPQRSTTJVWXYZ
0 026122 0 1220 0 6 <f (f-l) =42
The more usual mathematical notation for expressing $0 would be
Z
SI fi(fi-l), which is read as "the sum of all the terms for all integral
' i=A Z
values of f from A to Z inclusive. In turn, fi(fi-l) would be expanded
"* ' i=A
as fACfA-l)-** ■**fc(fC“ 1 ) + » • • • .+.fz(fz~ 1 ) * However, in the
interest of simplicity the notation if (f-l) is employed; likewise, the
notations (fa* and <f>p are employed in lieu of the more usual E($ r ) and E(<j)p) .
^ Another method of determining the relative monoalphabetic ity of a
cryptogram is based upon comparing the index of coincidence (abbr. X*C .)
of the cryptogram under examination with the theoretical I.C. of plain
text:* The I.C* of a message is defined as the ratio of <j> 0 to <fa*; thus,
in the example above, the I.C* is
188
"W
which equals 2* The theoretical
I*C. of English plain text is 1*73, which is the decimal equivalent of
j 2 £§£, the ratio of the " plain constant"
*03°5
I*C« of random text is 1, i.e., *038$ .
^0355
to the "random constant".
The
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51
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REF ID: A5 68 95
_ _ __« = W*25 *
( 2 ) ABCDEFGHIJKLrfNOPQRSTUVWXYZ
*0 002000600 02 00 0026 £f(f-l)sl8
Since ‘both distributions have 25 elements, then for hoth
4> r s .0385 x 25 x 24 s 21, and
4>P S .0667 X 25 X 24 s 4o.
Hence distribution (l) is monoalphabetic, while (2) is not*
e. The student most not assume that statistical tests in cryptanal-
ysis are infallible or absolute in themselves^"; statistical approaches
serve only as a means to the end, in guiding the analyst to the most
probably fruitful sources of attack. Since no one test in cryptanalysis
gives definite proof of a hypothesis (in fact, not even a battery of tests
gives absolute proof), all applicable statistical means at the disposal
of the cryptanalyst should be used; thus, in examination for monoalphabet-
icity, the <J> test, A test, and even other tests!9 could profitably be
employed. To illustrate this point, if the <j> test is taken on the
distribution of the plaintext letters of .the phrase
A QUICK BROWN FOX JUMPS OVER THE LAZY DOG
« = e N=33
ABCDEFGHIJKLMNOPQRSTUVWXYZ
2 2 12 2 2 *f(f-l)«20
4r = ^p s 70
it will be noticed that <J> 0 is less than half of 4r, thus conclusively
"proving" that the letters of this phrase could not possibly constitute
plain text nor a monoalphabetic encipherment of plain text in any lan-
guage! The student should be able to understand the cause of this
cryptologic curiosity.
18 ihe following quotation from the Indian mathematician P. C. Maha-
lanobis, concerning the fallibility of statistics, is particularly
appropriate in this connection: "If statistical theory is right, predic-
tions must sometimes come out wrong; on the other hand, if predictions
are always rightj then the statistical theory must be wrong."-- Sankhya,
Vol. 10, Part 3, p. 203. Calcutta, 1950.
19 One of these, the chi-square test , will be treated in a subsequent
text.
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28. Determining whether a cipher alphabet is standard (direct or
reversed) or mixed ,- -a. ' Assttmlxig that the militeral frequency distri-
bution for a given cryptogram has "been made, and that it shows clearly
that the cryptogram is a substitution cipher and is monoalphabetic in
character, a consideration of the nature of standard cipher alphabets 20
almost makes it obvious how an inspection of the distribution will dis-
close whether the cipher alphabet Involved is a standard cipher alphabet
or a mixed cipher alphabet* If the crests and troughs of the distribu-
tion occupy positions which correspond to the relative positions they
occupy in the normal frequency distribution, then the cipher alphabet
is a standard cipher alphabet* If this is not the case, then it is
highly probable that the cryptogram has been prepared by the use of a
mixed cipher alphabet • A mechanical test may be applied in doubtful
cases arising from lack of material available for study; just what this
test involves, and an illustration of its application will be given in
the next section, using specific examples*
b . Of course, if it has been determined that a standard cipher al-
phabet is involved in a particular instance, it goes without saying that
at the same time it must have been found whether the alphabet is a direct
standard or reversed standard cipher alphabet. The difference between the
distribution of a direct standard alphabet cipher and one of a reversed
standard alphabet cipher is merely a matter of the direction in which the
sequence of crests and troughs progresses— to the right, as is done in
normally reading or writing the alphabet (ABC ,"m Z), or to the left,
that is, in the reversed direction (Z C B A). With a direct standard
cipher alphabet the direction in which the crests and troughs of the dis-
tribution progress is the normal direction, from left to right; with a
reversed standard cipher alphabet this direction is reversed, from right
to left.
20 See par. 12.
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SECTION V
UNILITERAL SUBSTITUTION WITH STANDARD CIPHER ALPHABETS
Paragraph
Types of standard cipher alphabets.... *•••••«»•*•• ••••••*• 29
Procedure in encipherment and decipherment by means of
uniliteral substitution. 30
Principles of solution by construction and analysis of the
uniliteral frequency distribution.,..........*..*.*........*..... 31
Theoretical example of solution * 32
Practical example of solution by the frequency method ••••••••••••••• 33
Solution by completing the plain-component sequence *♦*.* ••••• 3^
Special remarks on the method of solution by completing the
plain-component sequence ••••••*• 3?
Value of mechanical solution as a short cut...*.**......*.***.***..* 36
Basic reason for the low degree of cryptosecurity afforded by
monoalphabet ic cryptograms involving standard cipher alphabets ... 37
29* Types of standard cipher alphabets .— a. Standard cipher
alphabets are of two types: ~
(1) Direct standard * in which the cipher component is the normal
sequence but shifted to the right or left of its point of coincidence in
the normal alphabet. Example:
►
Plain: ABCDEFGHIJKIMNOPQPSTUVWXIZ
Cipher: QRSTUWDCfZABCDEFGHIJKLMNOP
*
It is obvious that the cipher component can be applied to the plain
component at any one of 26 points of coincidence, but since the alphabet
that results from one of these applications coincides exactly with the
normal alphabet, a series of only 29 (direct standard) cipher alphabets
results from the shifting of the cipher component*
(2) Reversed standard, in which the cipher component is also the . .
normal sequence but runs in the opposite direction from the normal*
Example:
►
Plain: ABCDEEXrHIJKLMNOPQRSTUVWXYZ
Cipher: QPONMUCJIHGEEDCBAZIXWVUTSR
•4
Here the cipher component can be applied to the plain component at any
■of 26 points of coincidence, each yielding a different cipher alphabet.
There is in this case, therefore, a series of 26 (reversed standard)
cipher alphabets.
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55
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b. It is often convenient to refer to or designate one of a series
of cipher alphabets without ambiguity or circumlocution. The usual me-
thod is to indicate the particular alphabet to which reference 'is made by
citing a pair of equivalents in that alphabet, such as, in the example
above, Ap=Q c . The key for the cipher alphabet Just referred to, as
well as that preceding it, is Ap=Qc, and it Is said that the key letter
for the cipher alphabet is Qq.
c, The cipher alphabet in subpar. a(2), above, is also a reciprocal
alphabet ; that is, the cipher alphabet contains 13 distinct pairs of equiv-
alents which are reversible. For example, in the alphabet referred to,
A p sQc and Qp=A c ; Bp=P c and PpSB c , etc. The reciprocity exists through-
out the alphabet and is a result of the method by which it was formed.
(Reciprocal alphabets may be produced by Juxtaposing any two components
which are identical but progress in opposite directions .*5
30. Procedure in encipherment and decipherment by means of uni -
literal substitution. — a. When a message is enciphered by means of
uniliteral substitution , or simple substitution (as it is often called),
the individual letters of the message text are replaced by the single-
letter equivalents taken from the cipher alphabet selected by prearrange-
ment . Example :
Messages EIGHTEEN PRISONERS CAPTURFD
Enciphering alphabet: Direct standard, ApsT c
Plain: ABCDEFGHIJKIMTOPQRSTUVWXYZ
Cipher: TUVWXYZABCDEFGHIJKLMNOPQRS
Letter-for-letter encipherment:
EIGHTEEN PRISONERS CAPTURED
XBZAMXXG IKBLOGXKL VTMSKKW
The cipher text is then regrouped, for transmission, into groups of five.
Cryptogram:
XBZAM XXG3K BLHGX KLVTI MNKXW
b. The procedure in decipherment is merely the reverse of that in
encipEerment . The cipher alphabet selected by prearrangement is set up
with the cipher component arranged in the normal sequence and placed above
the plain component for ease in deciphering. The letters of the crypto-
gram are then replaced by their plaintext equivalents, as shown below.
Cipher: ABCDEFGHIJKU5N0PQPSTUVVDCYZ
Plain: HIJmfflOPQRSTUVWXYZABCIffiPG
The message deciphers thus:
Cipher: XBZAM XXGHC BLHGX KLVTI MNKXW
Plain: EIGHT EENFR ISONE RSCAP TUBED
The deciphering clerk rewrites the text in word lengths:
EIGHTEEN PRISONERS CAPTURED
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56
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REF ID: A5 68 95
c. In subpar, a, above, the ciyptogram was prepared in final form
for transmission by dividing the cryptographic text into groups of five.
This is generally the case in military communications involving cipher
systems. It promotes acc\ir?icy in telegraphic transmission since an opera-
tor knows he must receive s. definite number of characters in each group,
no more and no less. Also, xc ■ viually makes solution of the messages by
unauthorized persons more difficult because the length of the words,
phrases, and sentences of the plain text is hidden. If the last group of
the cipher text in subpar* 30 a had not been a complete group of five
letters, it might have been completed by adding a sufficient number of
meaningless letters (called nulls ) •
31. Principles of solution by construction and analysis of the
unlliteral frequency distribution . —a. The analysis of monoalphabetic
cryptograms prepared by the use of standard cipher alphabets follows al-
most directly from a consideration of the nature of such alphabets. Since
the cipher component of a standard cipher alphabet consists either of the
normal sequence merely displaced 1, 2, 3; . * * intervals from the normal
point of coincidence, or of the normal sequence proceeding in a reversed-
normal direction, it is obvious that the unlliteral frequency distribution
for a cryptogram prepared by means of such a cipher alphabet employed
monoalphabetically will show crests and troughs whose relative positions
and frequencies will be exactly the same as in the unlliteral frequency
distribution for the plain text of that cryptogram. The only thing that
has happened is that the whole set of crests and troughs of the distribu-
tion has been displaced to the right or left of the position it occupies
in the distribution for the plain text; or else the successive elements of
the whole set progress in the opposite direction. , Hence; it follows that',
the correct determination of the plaintext value of the cipher letter
marking any crest or trough of the uniliteral frequency distribution,
coupled with the correct determination of the relative direction in which
the plain component sequence progresses, will result at one stroke in the
correct determination of the plaintext values of all the remaining 25
letters respectively marking the other crests and troughs in that dis-
tribution. The problem thus resolves itself into a matter of selecting
that point of attack which will most quickly or most easily lead to the
determination of the value of one cipher letter. The single word
identification will hereafter be used for the phrase “determination of
the value of a cipher letter"; to identify a cipher letter is to find
its plaintext value.
b. It is obvious that the easiest point of attack is to assume that
the letter marking the crest of greatest frequency in the frequency
distribution for the cryptogram represents Ep. Proceeding from this
initial point, the identifications of the remaining cipher letters marking
the other crests and troughs are tentatively made on the basis that the
letters of the cipher component proceed in accordance with the normal
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57
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REF ID: A5 68 95
alphabetic sequence, either direct or reversed* If the actual frequency
of each letter marking a crest or a trough approximates to a fairly close
degree the normal or theoretical frequency of the assumed plaintext
equivalent, then the Initial identification 9c=Ep may he assumed to he
correct and therefore the derived identifications of the other cipher
letters also may he assumed to he correct.! If the original starting
point for assignment of plaintext values is not correct, or if the direc-
tion of "reading" the successive crests and troughs of the distribution
is not correct, then the frequencies of the other 25 cipher letters will
not correspond to or even approximate the normal or theoretical frequencies
of their hypothetical plaintext equivalents .on the basis of the initial
identification* A new initial point, that is, a different cipher equiv-
alent, must then he selected to represent Epj or else the direction of
"reading" the crests and troughs must he reversed. This procedure, that
is, the attempt to make the actual frequency relations exhibited hy the
unillteral frequency distribution for a given cryptogram conform to the
theoretical frequency relations of the normal frequency distribution in an
effort to solve the cryptogram, is referred to technically. as "fitting the
actual uniliteral frequency distribution for a cryptogram to the theoret-
ical unillteral frequency distribution for normal plain text", or, more
briefly, as " fitting the frequency distribution for the c r yptogram to the
normal frequency distribution ", or, still more briefly, '’ fitting the dis -
tribution to' the normal , 71 In statistical work the expression commonly
employed in connection with this process of fitting an acthal distribu-
tion to a theoretical one is "testing the goodness of fit." The goodness
of fit may be stated in various ways, mathematical in character. 2
c. In fitting the actual distribution to the normal. It is neces-
sary -to regard the cipher component (that is, the letters A . • . Z marking
the successive crests and troughs of the distribution) as partaking of
the nature of a circle, that is, a sequence closing in upon itself, so that
no matter with what crest or trough one starts, the spatial and frequency
relations of the crests and troughs are constant. This manner of regard-
ing the cipher component as being cyclic in nature is valid because it
is obvious that the relative positions end frequencies of the crests and
troughs of any unillteral frequency distribution must remain the same
regardless of what letter is employed as the initial point of the distri -
bution . Fig. 5 gives a clear picture of what is meant in this connect-
ion, as applied to the normal frequency distribution.
! The Greek letter 0 (theta) is used to represent a character or
letter without indicating its identity. Thus, instead of the circum-
locution "any letter of the plain text", the symbol 0p is used; and for
the expression "any letter of the cipher text", the symbol 0 C is used.
® One of these tests for expressing the goodness of fit, the % (chi)
test, will be treated in Military Cryptanalysis, Part II.
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58
■REF ID: A5 68 95
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g S: g ? ggg g 5 g
gasgggg^gg ggggg gggg55 g g^gggg
A B C D E F G H I J ;U TJ 0 ? Q R S ^ U ? H Y Z A F C D E F
g == „ g ggg gg = g-. Is, g
. ggggisg §-.55gggg ggggg gg^lgggssg
. . .FEDCBAZYXWVUTSRQPONMLKJIHGFEDCBA
Figure 5-
d. In the third sentence of subparagraph b, the phrase "assumed to
he correct" was advisedly employed in describing the results of the at-
tempt to fit the distribution to the normal, because the final test of
the goodness of fit in this connection (that is, of the correctness of
the assignment of values to the crests and troughs of the distribution)
is whether the consistent substitution of the plaintext values of the ci-
pher characters in the cryptogram will yield intelligible plain text* If
this is not the case, then no matter how close the approximation between
actual and theoretical frequencies is, no matter how well the actual fre-
quency distribution fits the normal, the only possible inferences are
that (l) either the closeness of the fit is a pure coincidence in this
case and that another equally good fit may be obtained from the same data,
or else (2) the cryptogram involves something more than simple monoalpha-
betic substitution by means of a single standard cipher alphabet. For
example, suppose a transposition has been applied in addition to the
substitution. Then, although an excellent correspondence between the
uniliteral frequency distribution a nd the normal frequency distribution
has been obtained, the substitution of the cipher letters by their assumed
equivalents will still not yield plain text. However, aside from such
cases of double encipherment, instances in which the uniliteral frequency
distribution may be easily fitted to the normal frequency distribution
and in which at the same time an attempted simple substitution fails to
yield Intelligible texfc are rare. It may be said that, in practical
operations whenever the uniliteral frequency distribution can be made to
fit the normal frequency distribution, substitution of values will result
in solution; and, as a corollary, whenever the uniliteral frequency
distribution cannot be made to fit the normal frequency distribvition,
the cryptogram does not represent a case of simple, monoalphabet ic
substitution by means of a standard alphabet.
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59
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REF ID: A5 68 95
32. Theoretical example of solution .— a. The foregoing principles
will become clearer by noting the encryption and solution of a theoretical
example. The following message is to be encrypted*
HOSTILE FORCE ESTIMATED AT ONE REGIMENT INFANTRY AND TWO PLATOONS
CAVALRY MOVING SOUTH ON QUINNIMONT PIKE STOP HEAD OF COLUMN NEARING ROAD
JUNCTION SEVEN THREE SEVEN COMMA EAST OF GREENACHE SCHOOL FIRED UPON BY
OUR PATROLS STOP HAVE DESTROYED BRIDGE OVER INDIAN CREEK.
b* First, solely for purposes of demonstrating certain principles,
the uniliteral frequency distribution for this plaintext message is
presented in Figure 6.
! 1 1
S .*iiL S S S
gssggggggg^ssggggg^ggggg^ §
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Figure 6.
a. Now let the foregoing message be encrypted monoalphabetically by
the following standard cipher alphabet, yielding the cryptogram shown
below and the frequency distribution sho^m in Figure 7*
Plain - - - - ABCDEFGHIJKLMNOPQRSTUVWXYZ
Cipher - - - GHIJKLMNOPQRSTUVWXYZABCDEF
Plain - - - HOSTI LEFOR CEEST IMATE DATON EREGI MEHTI NFANT RYAND
Cipher - - NUYZO EKLUX IKKYZ OSGZK JGZUT KXKMO SKTZO TLGTZ XEGTJ
Plain - - - TWOPL ATOON SCAVA LRYMO VINGS OUTHO NQUIN NBION TPIKE
Cipher - - ZCUVR GZUUT YIGBG RXESU BCTMY UAZNU TWAOT TOSUT ZVOQK
Plain - - - STOPH EADOF COLUM NNEAR INGRO ADJUN CTION SEVER THREE
Cipher - - YZWN KGJUL IURAS TTKGX OTMXU GJPAT IZOUT YKBKT ZHXKK
Plain - - - SEVEN COMMA EASTO FGREE NAbRE SCHOO IFIRE DUPON BYOUR
Cipher - - YKBKT IUSSG KGYZU LMXKK TGIXK YINUU RLOXK JAVUT HEUAX
Plain PATRO LSSTO PHAVE BESTR OYEDB RIDGE OVERI NDIAN CREEK
Cipher - - VGZXU RYYZU VNGBK JKYZX UEKJH XOJMK UBKXO TJOGT 33KKQ
Cryptogram
NUYZO
SKTZO
RXESU
Y Z U V N
IZOUT
LMXKK
VGZXU
UBKXO
R K L U X
TLGTZ
B 0 T M Y
KGJUL
YKBKT
T G I X K
RYYZU
TJOGT
IKKYZ
XEGTJ
UAZNU
IURAS
Z N X K IC
YINUU
VNGBK
I X K K Q
OSGZK
ZCUVR
TIAOT
TTKC-X
YKBKT
RLOXK
JKYZX
JGZUT
GZUUT
TOSUT
OTMXU
IUSSG
JAVUT
UEKJH
K X IC I-I 0
YIGBG
Z V 0 Q K
GJPAT
KGYZU
HEUAX
X 0 J II IC
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60
REF ID: A56895
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Figure 7*
d. Let the student now compare Figs. 6 and 7 # which have "been su- •
per imposed in Fig. 8 for convenience in examination. Crests and troughs
are present in "both distributions; moreover their relative positions and
frequencies have not been changed in the slightest particular. Only the
absolute position of the sequence as a whole has been displaced six
places to the right in Fig. J } as compared with the absolute position of
the sequence in Fig. 6.
e. If the two distributions are compared in detail the student will
clearly understand how easy the solution of the cryptogram would be to one
who knew nothing about how it was prepared. For example, the frequency of
the highest crest, representing Ep in Fig. 6 is 28; at an interval of four
letters before Ep there is another crest representing Ap with frequency
16. Between A and E there is a trough, representing the medium-frequency
letters B, C, D. On the other side of E, at an interval of four letters,
comes another crest, representing I with frequency l4. Between E and I
* there is another trough, representing the medium-frequency letters F, G, B.
Compare these crests and troughs with their homologous crests and troughs
in Fig. 7. In the latter, the letter K marks the highest crest in the
distribution with a frequency of 28; four letters before K there is an-
other crest, frequency 1 6 , and four letters on the other side of K there
is another crest, frequency l4. Troughs corresponding to B, C, D and F,
Gr, H are seen at H, I, J and L, M, B in Fig. 7* In fact, the two dis-
tributions may be made to coincide exactly, by shifting the frequency
distribution for the cryptogram six places to the left with respect to
the distribution for the equivalent plaintext message, as shown herewith.
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REF ID: A5 68 95
ABCDEFGHIJKLMNOPQRSTUVWXYZ
2
M
=5 g
6 5 5 5 S 5 S S
& g 5= § g - g - g g
gi:ggggggg-=:ggggg-ggggg«- §
GHIJKLMNOPQRSTUVWXYZABCDEF
Figure 9.
f. Let us suppose now that nothing is known about the process* of
encryptions and that only the cryptogram and its uniliteral frequency
distribution is at hand# It is clear that simply bearing in mind the
spatial relations of the crests and troughs in a normal frequency dis-
tribution would enable the cryptanalyst to fit the distribution to the
normal in this case. He would naturally first assume that K c sEp, from
which it would follow that if a direct standard alphabet is involved,
LcsFpjMcssGpi and so on, yielding the following (tentative) deciphering
alphabet:
Cipher ABCDEFGHIJKLMNOPQRSTUVWXYZ
Plain UVWXYZABC D.,33 FGHIJKLMNOPQRST
■r *
jg. Now comes the final tesii £f these assumed values are substi-
tuted in the cipher text, the plain text immediately appears. Thus:
NUYZO RKLUX IKKYZ OSGZK JGZUT etc.
HOSTI LEFOR GEEST I MATE DATON etc.
h. It should be clear, therefore, lhat the initial selection of
Gc as the specific key (that is, to represent Ap) in the process of
encryption has absolutely no effect upon the relative spatial and
frequency relations of the crests and troughs of the frequency distri-
bution for the cryptogram. If Qc had been selected to represent Ap,
these relations would still remain the same, the whole series of crests
and troughs being merely displaced further to the right of the positions
they occupy when Gc«Ap.
33. Practical example of solution by the frequency method .—
a. The case of direct standard alphabet ciphers . — (1) The following
cryptogram is to be solved by applying the foregoing principles:
N W N V H
W B N J B
C A X X Y
C X 0 W N
B J C C J
F C X W B
L T R W P
«
C X Y Y N
X D A Y X
C IT A B L
B R C R X
X U R W 0
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' (2) From the presence of so mars/ low-frequency letters such as B,
W, and X it Is at once suspected that this is a substitution cipher. But
to illustrate the steps, that must he taken in difficult cases in order to
he certain in this respect, a uniliteral frequency distribution is con-
structed, and then reference is to Charts 2 to 5 to note whether the
actual numbers of vowels, high-, m&uU—-, end low-frequency consonants
fall inside or outside the areas 5 ^limited by the respective curves •
= _ _ s 9 g = _ S
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Figure 10 a.
Letters
Frequency
Position with respect to areas
delimited by curves
Vmrftla (iRTflJIY)
* 10
is
26
12
Outside, chart 1.
Outside, chart 2.
Outside, chart 3.
Outside, chart 4.
Higb-frfirjuency Cnnnnn n.nfa (D R S T)
Medium-frequency Consonants (BCFGHLMPV ff) —
Tjniv-frRqiiftnr.y finnarmimts i(JKQX2)
Total .
60
1
(3) All four points falling completely outside the areas delimited by
the curves applicable to these four classes of letters, the cryptogram is
clearly a substitution cipher,
(4) The appearance of the frequency distribution, with marked crests
and troughs, indicates that the cryptogram is probably monoalphabetic . At
this point the <f> test is applied to the distribution. The observed value
of <f> is found ^o be 258, while the expected value of <f> plain and <j) random
are calculated to be 236 and 136, respectively. The fact that the ob-
served value is not only closer to but greater than <J>p is taken as
statistical evidence that the cryptogram is monoalphabetic. Furthermore,
reference being made to Chart 6 , the point of intersection of the message
length (60 letters) and the number of blanks (8) falls directly on
curve P; this is additional evidence that the message is probably mono-
alphabetic •
(5) The next step is to determine whether a standard or a mixed
cipher alphabet is involved. This is done by studying the positions and
the sequence of crests and troughs in the frequency distribution, and
trying to fit the distribution to the normal.
63
REOTIUCTED'
REF ID: A5 68 95
(6) The first assumption to Tie made is that a direct standard cipher
alphabet is involved. The highest crest in the distribution occurs over
Xq. Let it he assumed that X c =Ep. Then Y c , Z c , Aq, • • . . =Fp, Gp,
Hp, . • * ., respectively; thus:
_ _ S cs g = _ s 000
Cipher. ...A BCDEFGHIJKLMN0PQRSTUV¥XYZ
Plain H IJKLMNOPQRSTUVWXYZABCDEFG
Figure 10b.
“ t
It may he seen quickly that the approximation to the expected frequencies
is very poor. There are too many occurrences of Jp, Qp, Up and Fp and
too few occurrences of Up, Op, Rp, Sp, T p and Ap. Moreover, if a substi-
tution is attempted on this oasis, the following is obtained for the first
two cipher groups:
Cipher N WNVHCAXXY
"Plain text"U DUCO JHEEF
This is certainly not plain text and it seems clear that X c is not E_, if
the hypothesis of a direct standard alphabet cipher is correct. A
different assumption will have to he made.
(T) Suppose C c aEp. Going through the same steps as before, again
no satisfactory results are obtained. Further trials^ are made along the
same lines, until the assumption N c sEp is tested:
gjf sr __ == ^ 5
Cipher. ...A BCDEFGHIJKLMNOPQRSTUV¥XYZ
Plain.. *..R STUVWXYZABCDEFGHIJKLMNOPQ
*
Figure 10c.
(8) The fit in this case is quite good; possibly there are too few
occurrences of Ap, Dp, and Rp. But the final test remains: trial of the
substitution alphabet on the cryptogram itself. This is done and the
results are as follows:
C:
N W N V H
C A X X Y
B 3 C C J
L T R W P
X D A Y X
B R G
R
X
P:
ENEMY
TROOP
S A T I A
CKING
0 U R P 0
SIT
I
0
C:
W B N J B
C X 0 W N
F C X W B
C X Y Y N
C N A B L
X U R
¥
0
P:
N S E A S
T 0 F N E
¥ T 0 N S
T 0 P P E
T E R S C
0 L I
N
F
ENEMY TROOPS ATTACKING OUR POSITIONS EAST OF NEWTON. PETERS COL 3UF*
3 It is unnecessary, of course, to write out all the alphabets and
pseudo-decipherments, as shown above, when testing assumptions. This is
usually done mentally.
IiEQTIlICTED
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REF ID: A5 68 95
(9) It is always odvieablc to note tho specific key. In this case
the correspondence between any plaintext letter and its cipher equivalent
will indicate the key. Although other conventions ore possible, and
equally valid, it is usual, however, to indicate the key by noting the
cipher equivalent of Ap. In this case Ap- J c ,
b. The case of reversed standard alphabet ciphers «--(l) Let the
following cryptogram and its frequency distribution be studied.
F W F X L
W R F J R
QSVVU
Q V E W F
RJQQJ
II Q V W R
H Z B W D
Q V U U F
V P S U V
Q F S R H
RBQBV
yiBRE
(2) The preliminary steps illustrated above. Trader stibpar. a (l)
to (4) inclusive, in connection with the test for class and monoalphabet-
lcity, will here be omitted, since they are exactly the same in nature.
The result is that the cryptogram is obviously a substitution cipher and
is monoalphabetic •
(3) Assuming that it is not known whether a direct or a reversed
standard alphabet is involved, attempts are at once made to fit the fre-
quency distribution to the normal direct sequence. If the student will
try them he will soon find out that these are unsuccessful. All this
takes but a few minutes.
(4) The next logical assumption is now made, viz ., that the cipher
alphabet is a reversed standard alphabet. When on this basis F c is
assumed to be Ep, the distribution con readily be fitted to the normal,
practically every crest and trough in the actual distribution correspond-
ing to a crest or trough in the expected distribution.
s a 2 _ _ _ isi^:
Cipher. ...A BCDEFGHIJKLMNOPQRSTUVWXYZ
Plain JIHGFEDCBAZYXWVUTSRQPONMLK
Figure lOd.
(5) When the substitution is made in the cryptogram, the following
is obtained.
Cryptogram... F WFXL QSVVU RJQQJ
Plain text • • «E NEMY TROOP SATTA
(6) The plaintext message is Identical with that in subpar. a. The
specific key in this case is also Ap=J c . if the student Trill compare the
frequency distributions in the two cases, he Trill note that the relative
positions and extents of the crests and troughs are identical; they
merely progress in opposite directions.
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REF ID: A5 68 95
e. General note on solution by the frequency method .-- In actual
practice, the procedure of subpars . a and b are given a more rapid treat-
ment than that just described, the practical treatment being based, not
on the initial finding of some single crest or trough, but rather on locat-
ing the more readily-disoernlble clusters of crests which usually appear
in a distributio n, su ch as the distinctive crest-patterns representing
"A,.^#..!" and "RST" . These crest-patterns are searched for, with a
quick scanning of the distribution, and then the relative placement with
respect to each other is tested to see if it conforms to the expectation
for a direct standard cipher alphabet, and, if not, then for a reversed
standard cipher alphabet. During this latter step, which consists of
little more than counting in one direction and then (when necessary) in
the other, the blank (or near ly-bla rik) expectation of "UTC’ 1 followed by
the characteristic curve for "IM'KiKP" and the blank "Q" are considered,
as a means of either substantiating or invalidating the original
"identification" of the crests,
34. Solution by completing the plain-component sequence . --
a. The case of direct standard alphabet ciphers .— (l) The foregoing
method of analysis, involving as it does the construction of a uniliteral
frequency distribution, was termed a solution by the frequency method
because it Involves the construction of a frequehby distribution and its
study. There is, however, another method which is much more rapid, almost
wholly mechanical, and which, moreover, does not necessitate the con-
struction or study of any frequency distribution whatever. An under-
standing of the method follows from a consideration of the method of
encipherment of a message by the use of a single, direct standard cipher
alphabet*
( 2 ) Note the following encipherment:
Message TWO CRUISERS SUM
Enciphering Alphabet
Plain ABCDEFGHIJKLM.HOPQRSTUVWXYZ
Cipher GHIJKLMNOPQRSTUVWXYZABCDEF
Encipherment
Plain text TWO CRUISERS SUNK
Cryptogram ZCU IXAOYKXY Y AT Q
Cryptogram
ZCUIX AOYKX YYATQ
(3) The enciphering alphabet shown above represents a cc.sc wherein
the sequence of letters of both components of the cipher alphabet is the
normal sequence, with the sequence forma the cipher component merely
shifted si:: places to the left (or 20 positions to the right) of the
position it occupies in the normal alphabet. If, th.oref ci e, two strips
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66
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REF ID: A5 68 95
of paper bearing -fche letters of the normal sequence, equally spaced, are
regarded as the two components of the cipher alphabet and are juxtaposed
at all of the 25 possible points of coincidence, it is obvious that one
of those 25 juxtapositions must correspond to the actual juxtaposition
shown in the enciphering alphabet directly above . It is equally obvious
that if a Record were kept of the rc wilts obtained by applying the values
given at each juxtaposition to the letters of the cryptogram, one of these
results would yield the plain text of the cryptogram.
(4) Let the vork be systematized and the results set down in an
orderly manner for examination. It Is obviously unnecessary to juxtapose
the two components so that A c sA~, for on the assumption of a direct stan-
dard alphabet, juxtaposing two direct normal components at their normal
point of coincidence merely yields .plain text . The next possible juxta-
position, therefore, is Ac»Bp. Let the juxtaposition of the two eliding
strips therefore be A c =Bp, as shown here:
Plain i®CIM?GHIJKIMfOPQPSTUVWXYZ
Cipher— ABCDEFGHIJKLMNOPQBSTUYWXyZABCDEFGHIJKIM^OPQf^TUVVDCYZ
The values given by this juxtaposition are substituted for the letters
of the cryptogram and the following results are obtained.
Cryptogram ZCUIX AOYKX YYATQ
1st' Test— 1 "Plain text’ 1 A D V J Y B P Z L Y Z Z B U R
This certainly is not intelligible text; obviously, the two components
were not in the position indicated In this first test. The plain
component is therefore slid one interval to the left, making Ac=Cp, and
a second test is made. Thus
Plain ABCDEFGHIJICLMNOPQRSTUVWXYZ
Cipher — ABCDEFGHIJKLMOPQRSTUVWXYZABCDEFGHIJECIMHOPQPSTUVWXXZ
Cryptogram ZCUIX AOYKX YYATQ
2d Test— "Plain text" B E W K Z C Q A M Z A A C V S
Neither does the second test result in disclosing any plain text. But,
If the results of the two tests are studied a phenomenon that at first
seems quite puzzling comes to light. Thus, suppose the results of the
two tests are superimposed in this fashion.
Cryptogram ZCUIX AOYKX YYATQ
1st Test— —"Plain text" A D V J Y B P Z L Y Z Z B U R
2d Test "Plain text" BEWKZ CQAMZ AACVS
One of the strips should bear the sequence repeated. This permits
juxtaposing the two sequences at all 2 6 possible points of coincidence
so as to have a complete cipher alphabet showing at all times.
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REF ID: A5 68 95
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(5) Note what has happened* The net result of the two experiments
was merely to continue the normal sequence begun hy the cipher letters at
the heads of the columns of letters. It is obvious that if the normal
sequence is completed in each column the results will be exactly the same
as though the whole set of 23 possible tests had actually been performed .
Let the columns therefore be completed, as shown in Fig. 11.
ZCUIXAOYKXYYATQ
ADVJYBPZLYZZBUR
BEWKZCQAMZAACVS
CFXLADJRBNABBDWT
DGYMBESCOBCCEXU
EHZNCFTDPCDDFYV
FIAODGUEQDEEGZW
. GJBPEHVFREFFHAX
HKCQFIWGSFGGIBY
ILDRG JXHT6HHJCZ
JMESHKYIUHIIKDA
KNFT ILZJVIJJLEB
LOGUJMAKW JKKMFC
MPHVKHBLXKLLNGD
NQIWLOCMYLMMOIIE
ORJXMPDNZMNNPIF
PSKYNQEOANOOQJG
QTLZORFPBOPPRICH
RUMAPSGQCPQQSLI
SVNBQTHRDQRRTMJ
0 C RU I S B B S SUNK
UXPDS V JTFSTTVOL
VYQETWKUGTUUWPM
W Z R F U X L V H U V V X Q N
XASGVYMWIVWWYBO
YBTHYTZNXJWXXZSP
Figure 11.
An examination of the successive horizontal lines of the diagram discloses
one and only one line of plain text, that marked by the asterisk and read-
ing TWOCRUISERSSUNK.
(6) Since each column in Fig. 11 is nothing but a normal sequence,
it is obvious that instead of laboriously trriting down these columns of
letters every time a cryptogram is to be examined, it would be more con-
venient to prepare a set of strips each bearing the normal sequence
doubled (to permit complete coincidence for an entire alphabet at any set-
ting), and have them available for examining any future cryptograms. In
using such a set of sliding strips in order to solve a cryptogram prepared
by means of a single direct standard cipher alphabet, or to make a test to
determine whether a cryptogram has been so prepared, it is only necessary
to "set up" the letters of the cryptogram on the strips, that is, align
them in a single row across the strips (by sliding the individual strips
68
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REF ID : A56895
up ox' down) . The successive horizontal linos, called Generatrices (sin-
gular, generatrix ) 5 , are then examined in a search for intelligible text.
If the cryptogram really "belongs to this simple type of cipher, one of
the generatrices will exhibit intelligible text all the way across; this
text will practically invariably the plain text of the message. This
method of analysis may he termed & solution by completing the plain -
component sequence . Sometimes it is referred to as 1 ' running down* '~t he
sequence. The px'inciple upon which the method is based constitutes one
of the cryptanalyst’s most valuable tools
b. The case of reversed standard alphabets . — ( 1 ) The method describ-
ed under subpar. a may also be applied, in slightly modified form, in the
case of a cryptogram enciphered "by a single reversed standard alphabet.
The basic principles are identical in the two cases, as will now be demon-
strated.
(2) Let two sliding components be prepared as before, except that in
this case one of the components must be a reversed normal sequence, the
other, a direct normal sequence.
(3) Let the two components be juxtaposed A to A, as shown below,
and then let the resultant values be substituted for the letters of the
cryptogram. Thus :
CRYPTOGRAM
NKSEP MYOCP 0 0 M T W
Plain ABCDEPGHIJKLMOPQRSTUV^-TXYZ
C ipher ZmrVTITSRqP0MiUCJmGFE]XnBAZmrra?SR0P0mCKJIHG]^IXn3A
Cryptogram NKSEP MYOCP OOMTW
1st Test— ’'Plain text 1 ’ IT Q I W L 0 C M Y L M M 0 H E
(h) This does not yield intelligible text, and therefore the revers-
ed component is slid one space forward and a second test is made. Thus:
Plain ABCDEFGHIJKIMIOPQRSTtJ\A-JYYZ
Cipher ZYXtmiTSROpOmjQlCJIHGEEDCBAZmmJTSRG^OM.ILKJIHGEEDCBA
Cryptogram H K S E 13 MYOCP OOMTW
2d Test “Plain text" 0 R J X M PDHZM II N P IP
(5) Neither does the second.' test yield intelligible text. But let
the results of the two tests he superimposed. Thus:
Cryptogram NKSEP MYOCP 0 0 M $7 W
1st Test— "Plain text" N 0, I W L 0 C M Y L M M O H E
2d Test — “Plain text" ORJXM PDNZM NNPIF
^ Pronounced: jSn'er-a-tri'sez and jen' er-a/tr^ks , respectively.
r ■■ — — — — - ■
0 A set of heavy paper strips, suitable for use in completing the
plain-component sequence, has "been prepared for use as a training aid in
connection with the courses in Military Cryptanalysis.
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(6) It Is seen that the letters the "plain text" given by the
second trial are merely the continuants of the normal sequences Initiated
by the letters of the "plain text" given hy the first trial# If these
sequences are "run down"— that is, completed within the columns— the
results must Obviously be the same as though successive tests exactly
similar to the first two were applied to the cryptogram, using one
reversed normal and one direct normal component# If the cryptogram has
really been prepared by means of a single reversed standard alphabet,
one of the generatrices of the diagram that results from completing the
sequences must yield Intelligible text#
(7) Let the diagram be made, or better yet, if the student has
already at hand the set of sliding strips referred to in footnote 6 to
page 69, let him "set up" the letters given by the first trial# Pig* 12
shows the diagram and indicates the plaintext generatrix.
KKSEPMYOCPOOMTW
H Q I W L 0 0 M Y L k M 0 H E
ORJXMPDNZMNEPIF
PSKYNQEOANOOQJG
QTLZORFPBOPPRKH
RUMAPSGQCPQQSLI
SVNBQTHRDQRRTMJ
*TWOCRUISERSSTJHK
UXPDSV JTFSTTVOL
VYQETWKUGTUUWPM
WZRFUXLVHUVVXQN
XASGViYMW IVWWYRO
YBTHWZNXJWXXZSP
ZCUIXAOYKXYYATQ
ADV JYBPZLYZZBUR
BEWKZC QAMZAACV S
CFXLADRBNABBDWT
DGYMBESCOBCCEXU
EHZNCFTDPCBDFYV
FIAODGUEQDEEGZW
GJBPEHVFREFFHAX
HKCQFIWGSFGGIBY
ILDRGJXHTGHHJCZ
JMESHKYIUHIIKDA
KNFTILZJVIJJLEB
LOGUJMiAKWJKKMFC
MPHVKNBLXKLLNGD
Figure 12.
(8) The only difference in procedure between this case and the
preceding one (where the cipher alphabet vas a direct standard alphabet)
is that the letters of the cipher text ape first "deciphered" by means
of any reversed standard alphabet and then the columns are "run down",
according to the normal A B C . * . Z sequence. For reasons which will
REF ID: A5 68 95
■become apparent very soon, the first step in this method is technically
termed converting the cipher letters into their plain-component equiva-
lents; the second step is the same as before,
component sequence.
ecial remarks on the method of soluti
_ _ i _^ —a. The terms employed to designate the steps
in the solution set forth in par, 34b (8), viz ,, "converting the cipher
letters into their plain-component equivalents" and "completing the plain-
component sequence", accurately describe the process. Their meaning will
■become more clear as the student progresses with the work. It may "be said
that whenever the components of a cipher alphabet are known sequences, no
matter how they are composed, the difficulty and time required to solve
any cryptogram involving the use of those components is considerably re-
duced, In some cases this knowledge facilitates, and in other cases is
the only thing that makes possible, the solution of a very short cryptogram
that might otherwise defy solution . Later on an example wxll be given to
illustrate what is meant in this regard.
b, ( The student should take note, however, of two qualifying expres-
slons”that were employed in a preceding paragraph to describe the results
of the application of the method. It was started that "one of the gener-
atrices will exhibit intelligible text all the way across ; this text will
practically invariably be the plain text." Will there 'ever he a case in
which more than one generatrix will yield intelligible text through its
extent? That obviously depends almost entirely on the number of letters
that are aligned to form a generatrix. If a generatrix contains but a
very few letters, only five, for example, it may happen as a result of
pure chance that there will be two or more generatrices showing what
might be "intelligible text," Note in Fig, 11 , for example, that there
are several cases in which 3-letter ‘and 4-letter English words (LAD, COB,
MESH, MAPS, etc,) appear on generatrices that are not correct, these
words being formed by pure chance. But there is not a single case, in this
diagram, of a 5-letter or longer word appearing fortuitously, because
obviously the longer the word the smaller the probability of its appear-
ance purely by chance; and the probability that two generatrices of 15
letters each will both yield intelligible text along their entire length
is exceedingly remote, so remote, in fact, that in practical cryptology
such a case may be considered nonexistent .7
£« The student should observe that in reality there is no difference
whatsoever in principle between the two methods presented in subpars, a
and b of par, 34* In the former the preliminary step of converting the
cipher letters into their plain-component equivalents is apparently not
present but in reality it is there. The reason for its apparent absence
is that in that case the plain component of the cipher alphabet is ident-
ical in all respects with the cipher component, so that the cipher letters
T A person with patience and an inclination toward the curiosities of
the science might construct a text of 15 or more letters which would yield
two " intelligible" texts on the plain-component completion diagram.
71
REF ID: A5 68 95
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require no conversion, or, rather, they are identical with the equivalents
that would result if they were converted on the basis A c sAp, In fact, if
the solution process had been arbitrarily initiated by converting the ci-
pher letters into their plain-component equivalents at the setting AcsOp,
for example, and the cipher component slid one interval to the right
thereafter, the results of the first and second tests of par, 34a would
be as follows:
Cryptogram ZCUIXAO YKXYIATQ
isT! Test— "Plain text" — N Q I W LOC MY L M M OH E
2d Test— "Plain text" — ORJXMPBRZMNNPIF
Thus, the foregoing diagram duplicates in every particular the diagram
resulting from the first two tests under par, 34b: a first line of cipher
letters , a second line of letters derived from them but showing externally
no relationship with the first line, and a third line derived immediately
from the second line by continuing the direct normal sequence, ‘ TM*i '*bint
is brought to attention only for the purpose of showing that a sivye,
broad principle is the basis of the general method of solution by complet-
ing the plain -component sequence, and once the studtiri has this ’’trialy in
mind he will have no difficulty whatsoever in realizing whe? j .principle
is applicable, what a powerful crypt analytic tool it can be, and what
results he may expect from its application in specific instances,
d. In the two foregoing examples of the application of the prin-
ciple, the components were normal sequences j but it should he clear to
the student, if he has grasped what has been said in the preceding sub-
paragraph, that these components may be mixed sequences which, if known
(that is, if the sequence of letters comprising the sequences is known to
the cryptanalyst) , can be handled just as readily as can components that
are normal sequences.
e. It is entirely immaterial at what points the plain and the cipher
components are juxb&posed in the preliminary step of converting the cipher
letters into their plain-component equivalents. For example, in the case
of the reversed alphabet cipher solved in par* 34b, the two components
were arbitrarily juxtaposed to give the value ApsAc, but they might have
been juxtaposed at any of the other 25 possible points of coincidence
without in any way affecting the final result, viz ., the production of
one plaintext generatrix in the completion diagram.
3 6, Value of mechanical solution as a short cut .— a. It is evident
that the very first step the student should take in his attempts to solve
an unknown cryptogram that is obviously a substitution cipher is to try
the mechanical method of solution by completing the plain-component se-
quence, using the normal alphabet, first direct, then reversed! This
takes only a very few minutes and is conclusive in its results . It saves
the labor and trouble of constructing a frequency distribution in case
the cipher is of this simple type. Later on it will be seen how certain
variations of this simple type may also be solved by the application of
this method. Thus, a very easy short cut to solution is afforded, which
even the experienced cryptanalyst never overlooks in his first attack on
an unknown cipher.
" nnmr.Tnmnn
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REF ID : A56895
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b, It Is Important now to note that if neither of the two foregoing
attempts is successful in bringing plain text to light and tho cryptogram
is quite obviously monoalphabetic in character, the cryptanalyst is war -
ranted in assuming thab the, cryptogram involves a mixed cipher alphabet ,
37 » Basic reason for the low degree of ; .yptosecurity afforded by
mono alphabetic cryptograms involving standard cipher alphabets . --The
student has seen. that the solution of monoalphabetic cryptograms involving
standard cipher alphabets is a very easy matter. Two methods of analysis
were described, one involving the construction of a frequency distribu-
tion, the other not requiring this kind of tabulation, being almost mech-
anical in nature and correspondingly rapid. In the first of these two
methods it was necessary to make a correct assumption as to the value of
but one of the 2 6 letters of the cipher alphabet and the values of the
remaining 25 letters at once became known; in the second method it was not
necessary to assume a value for even a single cipher letter. The student
should understand what constitutes the basis of this situation, viz ., the
fact that the two components of the cipher alphabet are composed of known
sequences . What if one or both of these components are, for the crypt-
analyst, unknown sequences ? In other words, what difficulties will con-
front the cryptanalyst if the cipher component of the cipher alphabet is
a mixed sequence? Will such an alphabet be solvable as a whole at one
stroke, or will it be necessary to solve its values individually? Since
the determination of the value of one cipher letter in this case gives no
direct clues to the value of any other letter, it would seem that the
solution of such a cipher should involve considerably more analysis and
experiment than has the solution of either of the two types of ciphers so
far examined. The steps to be taken in the cryptanalysis of a mixed-
alphabet cipher will be dis cussed in the next section,
^ There is but one other possibility, already referred to under
subpar. 31d which involves the case where transposition and monoalphabetic
substitution processes have been applied in successive steps. This is
unusual, however, and will be discussed in its proper place.
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SECTION VI
UNILITERAL SUBSTITUTION WITH MIXED CIPHER ALPHABETS
Paragraph
Literal keys and numerical keys ••«..«.. •••«••••*. « 38
Types of mixed cipher alphabets •••••• * ••••••••••.*• . 39
Additional remarks on cipher alphabets.. ..•••*••••• 40
Preliminary steps in the analysis of a monoalphabet ic, mixed-
alphabet cryptogram. 4l
Preparation of the work sheet ' 42
Triliteral frequency distributions 43
Classifying the cipher letters Into vowels and consonants 44
Further analysis of the letters representing vowels and consonants*. 45
Substituting deduced values in the cryptogram, * ••••• ••••« 46
Completing the solution. 47
General remarks on the foregoing solution. • ...••• ••••.•••••••• 48
The "probable-word” method; its value and applicability. , 49
Solution of additional cryptograms produced by the same
components 50
Derivation of key words * ••.••••••••««••• 51
38. Literal keyB and numerical keys .— a. As has been previously
mentioned, most cryptosystems involve the use of a specific key to con-
trol the steps followed in encrypting or decrypting a specific message
(see subpar. $jb) • Such a key may be in literal form or in numerical form.
b . , It is convenient to designate a key which is composed of letters
as a literal key . As already mentioned, a literal key may consist of a
single letter, a single word, a phrase, a sentence, a whole paragraph, or
even a book; and, of course, it may consist merely of a sequence of let-
ters chosen at random,
c. Certain cryptosystems involve the use of a numerical key, which
may consist of a relatively long sequence of numbers difficult or impos-
sible for the average cipher clerk to memorize. Several simple methods
for deriving such sequences from words, phrases, or sentences have been
devised, and a numerical key produced by any of these methods is called a
derived numerical key (as opposed to a key consisting of randomly-selected
numbers) . One of the commonly-used methods consists of assigning numer-
ical values to the letters of a selected literal key in accordance with
their relative positions in the ordinary alphabet, as exemplified in the
following subparagraph .
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75
REF ID: A5 68 95
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d. Let the prearranged key word he the word LOGISTICS. Since C,
the penultimate letter of the key word, appears in the normal alphabet
before any other letter of the key word, it is assigned the number it
LOGISTICS
1
The next letter of the normal alphabet that occurs In the key word is G,
which is assigned the number 2. The letter I, which occurs twice in the
key word, is assigned the number 3 for its first occurrence and the num-
ber 4* for its second occurrence; and so on. The final result is:
LOGISTICS
562379418
This method of assigning the numbers is very flexible and varies with
different uses to which numerical keys are put. It may, of course, be
applied to phrases or to sentences, so that a very long numerical key,
ordinarly impossible to remember, may be thus derived at will from an
easily-remembered key text .
e. As far as the cryptanalyst is concerned, the derivation of a
numerical key from a specific literal key is of interest to him because
this knowledge may assist in subsequent solutions of cryptograms prepared
according to the same basic system, or in identifying the source from
which the literal key was selected - perhaps an ordinary book, a magazine,
etc. However, it should be pointed out that in some instances the crypt-
analyst may be unaware that a literal key has in fact been used as the
basis for deriving a numerical key.
39 « Types of mixed cipher alphabets .— a. It will be recalled that
in a mixed cipher alphabet the sequence of letters or characters in one
of the components (usually the cipher component) does not correspond to
the normal sequence. There are various methods of composing the. sequence
of letters or elements of this mixed component, and those which are based
upon a scheme that is systematic in its nature are very useful because
they make possible the derivation of one or more mixed sequences from any
easily-remembered word or phrase, and thus do not necessitate the carry-
ing of written memoranda. Alphabets involving a systematic method of
mixing are called systematically-mixed cipher alphabets .
b. One of the simplest types of systematically-mixed cipher alpha-
bets is the keyword-mixed alphabet . The cipher component consists of a
keyword or phrase (with repeated letters, if present, omitted alter
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76
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their first occurrence )•*•, followed by the letters of the alphabet in
their normal sequence (with letters already occurring in the key omitted
of course). Example, with GOVERNMENT as the keyword:
Plain: ABCDEFGHIJKIMNOPQRSTUVWXYZ
Cipher: GCTORNMTABCDFH1JKLPQSUWXYZ '' “
c. It is possible to disarrange the sequence constituting the
cipher component even more thoroughly by applying a simple method of
transposition to the keyword-mixed sequence. Two common methods are
illustrated below, using the key word TELEPHONY.
(l) Simple columnar transposition :
TELPHONY
ABCDFGIJ 1
KMQRSUVW !
X Z
Mixed sequence (formed by transcribing the successive columns from left
to right):
TAKXEBI'dZLCQPDRHFSOGUNIVYJW
(2) Numerically-keyed columnar transposition :
7-1-3-6-2-5-4-8
TELPHONY
ABCDFGIJ
KMQRSUVW
X Z
Mixed sequence (formed by transcribing the columns in a sequence deter-
mined by the numerical key derived from the key word itself) :
EBMZHFSLCQNIVOGUPDRrAKXYJW
Mixed alphabets formed by including all repeated letters of the
key word or key phrase in the cipher component were common in Edgar
Allan Poe *s day but are impractical because they are ambiguous, making
decipherment difficult ; an example:
Plain: ABCDEFGHIJJCLMNOPQRSTUVWXYZ
C ipher : NOWISTH^IMEFORALLGOODMENT
Cipher: ABCI^GHIJKIMNOPQPSTIJVWXXZ
Plain: P VHMSGD QJCAB OEF C
L J RWYN I
X T Z
TJ
The average cipher clerk would have considerable difficulty in decrypting
a cipher group such as TOOET, each letter of which has three or more
equivalents, and from which the plaintext fragments (N)HJTH., ..IT THI(S),
TP THI..., etc. can be formed on decipherment.
(a) Alphabet for enciphering.—
(b) Inverse form of (a),
for deciphering. — — — —
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d. The last two systematically-mixed sequences are examples of
transposition-mixed sequences . Almost any method of transposition may he
used to produce such sequences,
e. Another simple method of forming a mixed sequence is the deci -
mation method . In this method, letters in the normal alphabet, or in a
keyword-mixed sequence, are "counted off" according to any selected in-
terval. As each letter is decimated— that is, eliminated from the basic
sequence by counting off— it is entered in a separate list to form the
new mixed sequence. For example, to form a mixed sequence by this method|
from a keyword-mixed sequence based on the key phrase SBUG A SONG OF
SIXPENCE with 7 the interval selected, proceed as follows:
Keyword-mixed (or basic) sequence:
SINGAOFXPECBDHJKlMQPTUWyZ
'When the letters are counted off by 7 ’s from left to right, F will be the
first letter arrived at, H the second, T the third:
SINGAOy'XPECBDjfJKLMQR^UVWYZ
123^562123^56jri23^567
These letters are entered in a separate list (F first, H second, T third,
and so on) and eliminated from the keyword-mixed sequence. When the
end of the keyword-mixed sequence is reached, return to the beginning,
skipping the letters already eliminated:
S^NGAO^XP^CBDjfJKLtfQRTfUVWYZ
1 2 3 4 5
671234 562123 4 5 6 £
The decimation-mixed sequence:
FHTIEMZPQNIWCrVBSIXAGOKYJOT
f. Practical considerations, of course, set a limit to the complex-
ities that may be introduced in constructing systematically-mixed alpha-
bets. Beyond a certain point there is no object in further mixing. The
•greatest amount of mixing by systematic processes will give no more se-
curity than that resulting from mixing the alphabet by random selection,
such as by putting the 26 letters in a box, thoroughly' shaking them up,
and then drawing the letters out one at a time. Whenever the laws of
• chance operate in the construction of a mixed alphabet, the probability
of producing a thorough disarrangement of letters is very great. Random -
mixed alphabets give more cryptographic security than do the less compli-
cated systematically-mixed alphabets, because they afford no clues to
positions of letters, given the position of a few of them. Their chief
disadvantage is that they must be reduced to writing, since they cannot
readily be remenibered, nor can they be reproduced at will from an easily-
remembered key word.
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UOj. Additional remarks on cipher alphabets . --a. All cipher alpha-
bets may be classified on the basis of their arrangement as enciphering
or deciphering alphabets . An enciphering alphabet is one in which the
sequence of letters in the plain component coincides with the normal
sequence and is arranged in that manner for convenience in encipherment.
In a deciphering alphabet the sequence of letters in the cipher component
coincides with the normal, for convenience in deciphering. For example,
(l), below, shows a mixed cipher alphabet arranged as an enciphering al-
phabet; (2) shows the corresponding deciphering alphabet. An enciphering
alphabet and its corresponding deciphering alphabet present an Inverse
relationship to each other. To invert a deciphering alphabet is to write
the corresponding enciphering alphabet; to invert an enciphering alphabet
is to write the corresponding deciphering alphabet.
Enciphering Alphabet
f v Plain: ABCDEFGHIJKIMNOPQRSTUVWXyZ
Cipher: JKQVXZWESTRNUIOLGAPHCMYBDF
Deciphering Alphabet
, Cipher: ABCDEFGHIJKLMNOPQRSTUVWXyZ
< 2 ' Plain: KCOYHZ(^NABPVI.OSCKIJMDGEWF
b. A series of related reciprocal alphabets may be produced by
juxtaposing at all possible points of coincidence two components which
are identical, but progress in opposite directions. This holds regardless
of whether the components are composed of an even or an odd number of
elements. The following reciprocal alphabet is one of such a series of
2 6 alphabets:
Plain: HJTORAULICBEFGJldlNOPQSTVWXZ
Cipher: GFEBCILUAI^yHZXWVTSQPONMKJ
A single or isolated reciprocal alphabet may be produced in one of two
ways:
(1) By constructing a complete reciprocal alphabet by arbitrary or
random assignments of values in pairs. That is, if Ap is made the
equivalent of K c , then Kp is made the equivalent of Ajj if Bp is made Rq,
then Rp is made B c , and so on. If the two components thus constructed
are slid against each other no additional reciprocal alphabets will be
produced.
(2) By juxtaposing a sequence comprising an even number of elements
against the same sequence shifted exactly half way to the right (or left),
as seen below:
ABCDEFGHIJKIMNOPQRSTUVWXyZ,
ABCDEFGHIJKLMH^OPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ
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REGTRICTEB -
7 n. Preliminary steps In the analysis of a monoalphabet ic , mixed -
alphabet cryptogram . — a. The student is now ready to resume his crypt-
analytic studies. Note the following cryptogram:
SFDZF IOGKL PZFGZ DYSEF HBZDS GVHTF UFLVD FGYVJ VFVHT GADZZ ATTYD ZYFZJ
2ZTGPT VTZBD VFHTZ DFXSB GIDZY VTXOI YVTEF VMGZZ THLLV XZDFM BTZAI TYDZY
BDVFH TZDFK ZDZZJ SXXSG ZYGAV FSLGZ ETHHT CDZRS VTYZD OZFFH TZAIT YDZYG
AVDGZ ZTK HI TYZ YS DZGHU ZFZTG UPGDI XWGHX ASR UZ DFU 3D EGHTV EAGXX
b. A casual inspection of the text disclosed the presence of sev-
eral long repetitions as well as of many letters of normally low fre-
quency, such as F, G, V, X, and Z ; on the other hand, letters of normally
high frequency, such as the vowels, and the consonants N and R, are rel-
atively scarce. The cryptogram is obviously a substitution cipher and
the usual mechanical tests for determining whether it is possibly of the
monoalphabetlc, standard-alphabet type are applied. The results being
negative, a uniliteral frequency distribution is immediately constructed,
as shown in Figure 13, and the <f> test is applied to it.
I §
A B
8 4
4>p=3668 (j> r =2iiT <{>0=3862
Figure 13.
c. The fact that the frequency distribution shows very marked
crests and troughs indicates that the cryptogram is very probably mono-
alphabetic, and the results of the <f> test further support this hypothesis.
The fact that the cryptogram has already been tested by the method of
completing the plain-component sequence and found not to be of the mono-
alphabetic, standard-alphabet type, indicates with a high degree of
probability that it involves a mixed cipher alphabet. A few moments might
be devoted to making a careful inspection of the distribution to insure
that it cannot be made to fit the normal; the object of this would be to
rule out the possibility that the text resulting from substitution by a
standard cipher alphabet had not subsequently been transposed. But this
inspection in this case is hardly necessary, in view of the presence of
long repetitions in the message.* (See subpar. 25g.)
1 g
g g g'g ? 'll
CDEFGHIJKLMNOPQRSTUVWXYZ
1 23 8 19 19 16 10 3 2 8 2 0 3 6 0 2 10 22 8 IS 1 8 14 35
^ This possible step is mentioned here for the purpose of making it
clear that the plain-component sequence completion method cannot solve a
case in which transposition has followed or preceded monoalphabet ic sub-
stitution with standard alphabets. Cases of this kind will be discussed
in a later text. It is sufficient to indicate at this point that the -
frequency distribution for such a combined substitution-transposition
cipher would present the characteristics of a standard alphabet cipher
and yet the method of completing the plain-component sequence would fail
to bring oub any plain texb.
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REF ID: A5 68 95
nEBTRICTED .
d. One might, of course, attempt to solve the cryptogram "by applying
the simple principles of frequency. One might, in other words, assume
that Z c (the letter of greatest frequency) represents Ep, D c (the letter
of next greatest frequency) represents T-n, and so on. If the message
were long enough this simple procedure might more or less quickly give
the solution. But the message is relatively short and many difficulties
would he encountered. Much time and effort would he expended unnecessar-
ily, because it is hardly to he expected that in a message of only 235
letters the relative order of frequency of the various cipher letters
should exactly coincide with, or even closely approximate the relative
order of frequency of letters of normal plain text found in a count of
50,000 letters. It is to he emphasized that the beginner must repress
the natural tendency to place too much confidence in the' generalized prin -
ciples of frequency and to rely too much upon them . It Is far better to
bring into effective use certain other data concerning normal plain text,
such as digraphic and trlgraphic frequencies.
h2» Preparation of the work sheet . — a. The details to he- considered
in this paragraph may at first appear to he superfluous, hut long expe-
rience has proved that systematization of the work and preparation of the
data in the most utilizahle, condensed form is most advisable, even if
this seems to take considerable time. In the first place, if it merely
serves to avoid Interruptions and irritations occasioned by failure to
have the data in an Instantly available form, it will pay by saving men-
tal wear and tear. In the second place, especially in the case of com-
plicated cryptograms, painstaking care in these details, while it may not
always bring about success, is often the factor that' is of greatest
assistance in ultimate solution. The detailed preparation of the data
may be irksome to the student, and he may be tempted to avoid as much of
it as possible, but, unfortunately, in the early stages of solving a
cryptogram he does not know (nor, for that matter, does the expert always
know) just which data are essential and which may be neglected. Even
though not all of the data may turn out to have been necessary, as a gen-
eral rule, time is saved in the end if all the usual data are prepared as
a regular preliminary to the solution of most cryptograms.
b. First, the cryptogram is recopied in the form of a work sheet .
This sheet should be of a good quality of paper so as to withstand con-
siderable erasure. If the cryptogram is to be copied by hand, cross-
section paper of -^-inch squares is extremely useful. The writing should
be in Ink, and plain, carefully-made roman capital letters should be used
in all cases .3 If the cryptogram is to be copied on a typewriter, the
ribbon employed should be impregnated with an ink that will not smear or
smudge under the hand.
3
It is advisable to use, for this purpose, the system of standardized
manual printing adopted by Service communications personnel. The use of
this system, which is included in Appendix 7, assures that work sheets
are completely legible, not only to the person preparing them, but to
others as well.
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c. The arrangement of the characters of the cryptogram on the work
sheet" - is a matter of considerable importance . If the cryptogram as first
obtained is in groups of regular length (usually five characters to a
group) onfl if the uniliteral frequency distribution shows the cryptogram
to be monoalphabetlc , the characters should be copied without regard to
this grouping. It is advisable to allow one space between letters (this
Is especially true for work sheets prepared on the typewriter), and to
write a constant number of letters per line, approximately 25. At least
two spaces, preferably three spaces, should be left between horizontal
lines, to allow room for multiple assumptions. Care should be taken to
avoid crowding the letters in any case, for this is not only confusing to
the eye but also mentally irritating when later it is found that not
enough space has been left for making various sorts of marks or indica-
tions . If the cryptogram is originally In what appears to be word lengths
(and this is the case, as a rule, only with the cryptograms of amateurs),
naturally it should be copied on the work sheet in the original group-
ings. If further study of a cryptogram shows that some special grouping
is required, it is often best to recopy it on a fresh work sheet rather
than to attempt to Indicate the new grouping on the old work sheet.
d. In order to be able to locate or refer to specific letters or
groups of letters with speed, certainty, and without possibility of con-
fusion, it is advisable to use coordinates applied to the lines and
columns of the texb as it appears on the work sheet. To minimize possi-
bility of confusion, it is best to apply letters to the horizontal lines
of the text, numbers. to the vertical columns^. In referring to a letter,
the horizontal line in which the letter is located is usually given first.
Thus, referring to the work sheet shown below, coordinates A17 designate
the letber Y, the 17th letter in the first line. The letter I is usually
omitted from the series of line indicators so as to avoid confusion with
the figure 1. If lines are limited to 25 letters each, then each set of
100 letters of the texb is automatically blocked off by remembering that
4 lines constitute 100 lebters.
e. Above each character of the cipher texb may be some indication
of the frequency of that character in the whole cryptogram. This indi-
cation may be the actual number of times the character occurs, or, if
colored pencils are used, the cipher letters may be divided up into three
categories or groups — high-frequency,* medium-frequency, and low-frequency.
It 'is perhaps simpler, if clerical help is available, to indicate the
actual frequencies. This saves constant reference to the frequency
tables, which interrupts the train of thought, and saves considerable
time In the end, since it enables the student better to visualize fre -
quency-patterns of words. In any case, it is recommended that the fre-
quencies of the letters comprising the repetitions be inscribed over their
■*' In some cryptosystems, certain low-frequency letters are employed as
word separators to indicate the end of a word; if the meaning of these
letters Is discovered, it is tantamount to having the cryptogram in word
lengths and thus the work sheet is made accordingly. See also in this
connection the treatment on word separators in Section VII .
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respective letters; likewise, tile frequencies of the first 10 and last 10
letters should also he inscribed, as these positions often lend themselves
readily to attack. ?
f. After the special frequency distribution, explained in Par. 1*3
belovj has been constructed, repetitions of digraphs and trigraphs should
be underscored. In so doing, the student should be particularly watchful
for trigraphlc repetitions which can be further extended into tetragraphs
and polygraphs of greater length. Repetitions of more than ten charac-
ters should be set off by heavy vertical lines , as they indicate repeated
phrases and are of considerable assistance in solution. If a repetition
continues from one line to the next, put an arrow at the end of the under-
score to signal this fact. Reversible digraphs and trigraphs should also
be indicated by an underscore with an arrow pointing in both directions.
Anything which strikes the eye as being peculiar, unusual, or significant
as regards the distribution or recurrence of the characters should be
noted. All these marks should, if convenient, be made with ink so as not
to cause smudging. The work sheet will now appear as shown below (not
all the repetitions are underscored):
1
2
3
4
6
0
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
10
10
23
35
10
10
3
10
15
6
5
35
19
19
35
23
14
10
5
19
15
4
35
23
10
A
s
F
«-
D
z
— >
F
I
0
G
H
L
p
z
F
G
z_
X
_Y
s
p
F
H
B
z
D
s
10
16
16
22
19
6
6
5
16
23
19
10
14
16
3
16
19
10
15
22
19
8
23
35
35
B
6
V
H
T
F
u
p
L
V D
F
G
Y
V
j
V
F
V
H
T
G
A
D
z
z
8
10
22
14
23
35
14
19
35
3
35
22
19
5
22
16
22
35
4
23
10
19
16
22
35
0
A
i
T
Y
D
z
Y
F
z
J.
z
T
G
p
T
V
T
z
B
D
V
F
H
T
z
23
10
8
4—
10
4
— »
10
10
23
35
14
16
22
8
8
10
14
10
22
3
19
10
2
10
35
35
D
D
« —
F
X
s
B
G
I
D
z
Y
V
T
X
0
I
Y
V
T
E
F
V
M
G
z
z
22
16
5
5
16
8
35
23
19
2
15
22
35
8
10
22
14
23
85
14
4
23
16
19
16
E
T
H
L
L
V
X
z_
D
F
M
H.
X
_z_
_A.
j_
X
X
X
x
_Y
B
X
x
X
x
22
35
23
19
2
35
23
35
35
3
10
8
10
10
19
35
14
19
8
is
10
10
5
19
35
F
JL
JL
D_
F
K
Z
D
Z
z
j
S
X
I
S
G
z
Y
G
A
V
F
S
L
G
z
V"
23
22
15
15
22
1
23
35
2
10
is
22
14
35
23
8
35
19
19
15
22
35
8
10
22
G
D
T
H
H
T
c
D
z
R
s
V
T
Y
Z
D
0
z
F
F
H_
X
z
A,
x
X
M
23
35
14
19
8
IS
23
19
35
35
22
2
15
10
22
14
35
14
10
23
36
19
15
5
H
( Y
_D_
z_
Y
G
A
V.
JL
_G
z
z
T
K
H
I_
X
Y
z
Y
S
D
z
G
H
u
35
19
85
22
19
5
s
10
23
10
8
1
10
16
8
8
10
2
6
85
23
19
6
10
23
J
Z
F
z
T
G
u
p
G
D
I
X
W
G
H
X
A
S
R
u
z
x
_F
u
I
D
3
10
16
22
is
3
8
19
8
8
K
E
G
H
T
V
E
A
G
X
X
^ See Appendix 4 in this connection.
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43. Trilateral frequency distributions .— a. In what has gone before,
a "type of frequency distribution known as a unilateral frequency distri-
bution was used. This, of course, shows only the number of times each
individual letter occurs . In order to apply the normal digraphic and
trigraphic frequency data (given in Appendix 2) to the solution of a
cryptogram of the type now being studied, it is obvious that the data
with respect to digraphs and trigraphs occurring in the cryptogram should
be compiled and should be compared with the data for normal plain text.
In order to accomplish this in suitable manner, it is advisable to con-
struct a more comprehensive form of distribution termed a triliteral
frequency distribution .”
b. Given a cryptogram of 50 or more letters and the task of deter-
mining what trigraphs are present in the cryptogram, there are three ways
in which the data may be arranged or assembled. One may require that the
data show (l) each letter with its two succeeding letters ; (2) each let-
ter with its two preceding letters; (3) each letter with one preceding
letter and one succeeding letter.
c. A distribution of the first of the three foregoing types may be
designated as a "triliteral frequency distribution showing two suffixes";
the second type may be designated as a "triliteral frequency distribution
showing two prefixes"; the third type may be designated as a "triliteral
frequency distribution showing one prefix and one suffix." Quadriliteral
and pentaliteral frequency distributions may occasionally be found useful.
d. Which of these three arrangements is to be employed at a specific
time depends largely upon what the data are intended to show. For present
purposes, in connection with the solution of a monoalphabetic substitution
cipher employing a mixed alphabet, possibly the third arrangement , that
showing one prefix and one suffix, is most satisfactory.
e. It is convenient to use jj-Inch cross-section paper for the con-
struction of a triliteral frequency distribution in the form of a distri-
bution showing crests and troughs, such as that in Figure l4. In that
figure the prefix to each letter to be recorded is inserted in the left
half of the cell directly above the cipher letter being recorded; the
suffix to each letter is inserted in the right half of the cell directly
above the letter being recorded; and in each case the prefix and the suf-
fix to the letter being recorded occupy the same cell, the prefix being
directly to the left of the suffix. The number in parentheses gives the
total frequency for each letter.
It is felt advisable here to distinguish between two closely related
terms. A triliteral distribution of A B C D E F would consider the
groups A B C, B C D, C D E, D E F; a trigraphic distribution would con-
sider only the trigraphs ABC and D E F. (See also subpar. 23d.)
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84
CONDENSED TABLE OF REPETITIONS
Digraphs
Trigraphs
Longer Polygraphs
DZ-9
TZ-5
-VF-4
DZY-4
FHT-3*
HTZAITYDZY-2
ZD-9
TY-5
VT— 4
HTZ-4
TYD-3
BDVFHTZDF— 2
HT— 8
FH— 4
ZF— 4
ITY-4
YDZ-3
ZAITYDZY— 3
ZY-6
GH-4
ZT— 4
' ZDF-4
ZAI-3 ’
FHTZ— 3
DF— 5
IT-4
ZZ-4
AIT-3
GZ-5
W
■
DU
ZZ
FH
ZF
VS
DK
VH
DM
EV
DX
VH
YZ
W
DG
TU
PH
VA ZG
DG ZI
TF SD
AX
EH
WH
PD
TU GT
ZH GX
DZ GU
YA KI
LZ FT
YA HT UD
SZ TH DX
MZ FT HT
BI MT AT
TP TL XS
TA FT AT
FY VT OY
SV VT GD ZS
GD HZ TD FZ TF SD OH GL FO
ABCDEFGHI
(8) (4) O) (23) (3) 08) 08) 00 00)
HV
ZG
IY
ZK
IY
HZ
V Y
HC
DH
HZ
IY
HZ
AR ZH
YD VE
RV VX
FL HZ
IG VZ
SG
UG
JX
PV
FI
FH
LV
GT
XB
ZG
RZ
JF
HL
DZ
UL
DG
IY
GP
YJ
PV
FH
XI
SF
SU
YP
HG
HZ
LD
HP
VG
IG
LZ
ZS
-F
HF
FP
GH
L
M
N
0
P
Q
R
S
T
U
V
(*)
(2)
(0)
(3)
(5)
(0)
CO
OO)
(22)
00
OS)
UD
FT
UF
DG
■ YY
ZT
GZ
DY
TA
OF
YD
DR
GD
GY
ZJ
DZ
KD
TD
DY
TA
XD
ZS ZT
TZ GZ
ZG DY
TD TD
TZ TB
ZG JT
X- ZB FJ
GX TD DY
HA IV ZA
IW ZV DZ
SI ZF BD
VZ TD GD
TO GV PF
XG FS PS DF
W X Y Z
0) (0 (14) (35)
JtQVXX It
S689SV : ai
REF ID: A5 68 95
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f . The trillteral frequency distribution is now to he examined with
a view to ascertaining what digraphs and trigraphs occur two or more
times in the cryptogram. Consider the pair of columns containing the
prefixes and suffixes to D c in the distribution, as shown in Fig. l4.
This pair of columns shows that the following digraphs appear in the
cryptogram:
Digraphs based on prefixes
(arranged as one reads up
the column)
FD, ZD, 2D, VD, AD, YD, BD,
ZD, ID, ZD, YD, BD, ZD, ZD,
ZD, CD, ZD, YD, VD, SD, CD,
ZD, ID
Digraphs based on suffixes
(arranged as one reads up
the column)
DZ, DY, D3, DF, DZ, DZ, DV,
DF, DZ, DF, DZ, DV, DF, DZ,
DT, DZ, DO, DZ, DG, DZ, DI,
DF, DE
The nature of the triliteral frequency distribution is such that in find-
ing what digraphs are present in the cryptogram it is immaterial whether
the prefixes or the suffixes to the cipher letters are studied, so long
as one is consistent in the study . For example, in the foregoing list of
digraphs based on the prefixes to D c , the digraphs FD, ZD, ZD, VD, etc.,
are found; if now, the student will refer to the suffixes of F c , Z c , V c ,
etc., he will find the very same digraphs indicated. This being the case,
the question may be raised as to what value there is in listing both the
prefixes and the suffixes to the cipher letters. The answer is that by
so doing the trigraphs are indicated at the same time. For example, in
the case of D c , the following trigraphs are indicated:
FDZ, ZDY, ZDS, VDF, ADZ, YDZ, BDV, ZDF, 3DZ, ZDF, YDZ, BDV, ZDF,
ZDZ, ZDT, CDZ, ZDO, YDZ, VDG, SDZ, GDI, ZDF,' IDE.
g. The repeated digraphs and trigraphs can now be found quite read-
ily. Thus, in the case of D c , examining the list of digraphs based on
suffixes, the following repetitions are noted:
DZ appears 9 times; DF appears 5 times; DV appears 2 times
Examining the trigraphs with D c as central letter, the following repeti-
tions are noted:
ZDF appears 4 times; YDZ appears 3 times; BDV appears 2 times
h. It is unnecessary, of course, to go through the detailed proce-
dure set forth in the preceding subparagraphs in order to find all the
repeated digraphs and trigraphs . The repeated trigraphs with D c as cen-
tral letter can be found merely from an inspection of the prefixes and
suffixes opposite D c in the distribution. It is necessary only to find
those cases In which two or more prefixes are identical at the same time
that the suffixes are identical. For example, the distribution shows at
once that in four cases the prefix to D c is Z c at -the same time that the
suffix to this letter is F c . Hence, the trigraph ZDF appears four times.
The repeated trigraphs may all be found in this manner.
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86
REF ID: A56895
RED TRIG TED
i. The most frequently repeated digraphs and trigraphs are then
assembled in what is termed a condensed table of repetitions , so as to
bring this information prominently before the eye. As a rule, in mes-
sages of average length, digraphs which occur less than four or five
times, and trigraphs which occur less than three or four times may be
omitted from the condensed table as being relatively of no importance in
the study of repetitions. In the condensed table the frequencies of the
individual letters forming the most important digraphs, trigraphs, etc,,
should be indicated,
44, Classifying the cipher letters into vowels and consonants .—
a. Before proceeding to a detailed analysis of the repeated .digraphs and
trigraphs, a very important step can be taken which will be of assistance
not only in the analysis of the repetitions but also in the final solu-
tion of the cryptogram. This step concerns the classification of the
high-frequency cipher letters into two groups — (l) those which most prob-
ably represent vowels, and (2) those which most probably represent con-
sonants. For if the cryptanalyst can quickly ascertain the equivalents'
of the four vowels, A, E, I, and 0, and of only the four consonants, R,
R, S, and T, he will then have the values of approximately two-thirds of
all the cipher letters that occur in the cryptogram.; the values of the
remaining letters can almost be filled in automatically.
b. The basis for the classification will be found to rest upon a
comparatively simple phenomenon: the as6ociational or combinatory be-
havior of vowels is, in general, quite different from that of consonants.
If an examination be made of Table 7-B in Appendix 2, showing the rela-
tive order of frequency of the 18 digraphs composing 25 percent of Eng-
lish telegraphic text, it will be seen that the letter E enters into the
composition of 9 of the 18 digraphs; that is, in exactly half of all the
cases the letter E is one of the two letters forming the digraph. The
digraphs containing E are as follows:
ED ER ER ES
HE RE SE TE VE
The remaining nine digraphs are as follows:
A T T HD OR ST
IN NT TH
OR TO
t
£. Rone of the 18 digraphs is a combination of vowels . Rote now
that of the 9 combinations with E, 7 are with the consonants R, R, S, and
T, one is with D, one is with V, and none is with any vowel . In other
words, Ep combines most readily with consonants but not with other vowels,
or even with itself. Using the terms often employed in the chemical ana-
logy, E shows a great "affinity" for the consonants R, R, S, T, but not
for the vowels. Therefore, if the letters of highest frequency occurring
in a given cryptogram are listed, together with the number of times each
of them combines with the assumed cipher equivalent of Ep> those which
show considerable combining power or affinity for the cipher equivalent
I
87
REF ID: A5 68 95
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of Ep may "be assumed to tie the cipher equivalents of N, R, S, Tpj those
which do not show any affinity for the cipher equivalent of Ep may he as-
sumed to he the cipher equivalents of A, I, 0, Up, Applying these prin-
ciples to the problem in hand, and examining the triliteral frequency
distribution, it is quite certain that Z<;=Ep, not only because Z c is the
letter of highest frequency, but also because it combines with several
other high-frequency letters, such as D c , »Cf G c> etc. The nine letters
of next highest frequency are:
23 22 19 19 16 15 14 10 10
DTFGVHYSI
Let the combinations these letters form with Z c be indicated in the fol-
lowing manner:
Number of times Z c =.
occurs as prefix — s
Cipher Letter D(23) T(22) F(l9) G(l9) V(l6) H(l5) Y(l4) S(l0) 1(10)
Number of times Z c pf 0 — % *”
occurs as suffix — S
d. Consider D c , It occurs 23 times in the message and l8 of those
times"~it is combined with Z c , 9 times In the form Z C D C (=E9p) , and 9 times
in the form DcZc (=9Ep) . It is clear that D c must be a consonant. In
the same way, consider T c , which shows 9 combinations with Z c , 4 in the
form ZcTc (=E0p) and 5 in the form T C Z C (=©Ep) . The letter T c appears to
represent a consonant, as do also the letters F c , G c , and Y c , On the
other hand, consider V c , occurring in all l6 times but never in combina-
tion with Z c j it appears to represent a vowel, as do also the letters He,
S c , and I c « So far, then, the following classification would seem logical:
Vowels Consonants
M=Ep), V c , H c , S c> I c D c , T c , F c , G c , Y c
Further analysis of the letters representing vowels and conso -
nants . — a. Op is usually the vowel of second highest frequency. Is it
possible to determine which of the letters V, H, S, I c is the cipher
equivalent of Op? Let reference be made again to Table 6 in Appendix 2,
where it is seen that the 10 most frequently occurring diphthongs are:
Diphthong 10 OU EA El AI IE AU EO AY UE
Frequency 4l 37 35 27 17 13 13 12 12 11
If V, II, S, I c are really the cipher equivalents of A, I, 0, Up (not
respectively), perhaps it is possible to determine which is which by
examining the combinations they make among themselves and with Z c T=Ep) •
Let the combinations of V, H, S, I, and Z that occur in the message be
listed. There are only the following:
ZZ c -Jj VHc — 2 HH C — 1 HI C — 1 IS C — 1 SV C — 1
ZZ C is of course EE^ . Note the doublet HH C ; if H c is a vowel, then the
chances are excellent that II c =0p because the doublets AA V) Up, UUp, are
practically non-existent, whereas the double vowel combination 00p is of
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REF ID : A56895
HEOTIUCTEB -
next highest frequency to the double vowel combination EEp. If H c =Op,
then Vc must "be Ip because the digraph VH C occurring two times in the
message could hardly be A0 p , or UOp, whereag the dipthong IOp is the one
of high frequency in English. So far then, the tentative (because so far
unverified) results of the analysis are as follows:
Zc»sEp H c sOp V c =I p
This leaves only two letters, I c and S c (already classified as vowels) to
be separated into A p and Up. Note the digraphs:
nic=oe p is c :ee p sv c =ei p
Only two alternatives are open:
(1) Either I c =Ap and S c =U p ,
(2) Or I c =U p and S^cAp#
If the first alternative is selected, then
HI c =0A p IS c =AU p SV c =UI p
If the second alternative is selected, then
HI c =OU p IS c =UAp SV c =AIp
The eye finds it difficult to choose between these alternatives; but sup-
pose the frequency values of the plaintext diphthongs as given in Table 6
of Appendix 2 are added for each of these alternatives, giving the follow-
ing:
HI c sOAp, frequency value: 7
SV c =UIt,, frequency values 5
IS c =AUp, frequency value =13
Total 25
Mathematically, the second alternative appears to be more probable than
the first .7 Let it be assumed to be correct and the following (still
tentative) values are now at hand:
Z c :E p II c =O p V c =l p S c =A p I c =U p
b. Attention is now directed to the letters classified as conso-
nants: How far is it possible to ascertain their values? The letter D c ,
from considerations of frequency alone, would seem to be Tp, but its
frequency, 23, is not considerably greater than that for T c . _It is not
7 A more accurate guide for choosing between the alternative groups
of digraphs could be obtained through a consideration of the . logarithmic
weights of their assigned probabilities, rather than their plaintext ”
frequency values . These weights are given in Appendix 2, along with an
explanation of the method for their derivation; a detailed treatment of
their application is presented in Military Cryptanalysis, Part II.
HI c :OUp, frequency value =37
SV c =A3p, frequency value =17
IS c =UA p , frequency values 5
Total 59
89
REF ID: A5 68 95
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much greater than bhat tor F c or S c , yith a frequency of 19 each. But
perhaps it is possible to ascertain not the value of one letter alone hut
of two letters at one stroke. To do this one may make use of a tetra-
graph of considerable importance in English, viz ., TIOHp . For if the
analysis pertaining to the vowels is correct, and if VHc=IOp, then an
examination of the letters immediately before and after the (digraph VH C
in the cipher text might disclose both Tp and Np. Reference to the text
gives the following:
GVUT 0 FVIEDq
' eioe p eio©p
The letter T c follows VH C in both cases and very probably indicates that
®c=Npi "but as to whether G c or F c equals Tp cannot be decided. However,
two conclusions are clear: first, the letter D c is neither Tp nor rip,
from which it follows that it must be either Rp or Spj second, the let-
ters Gc and F c must be either Tp and Sp, respectively, or Sp and Tp,
respectively, because the only tetragraphs usually found (in English)
containing the diphthong IOp as central letters are SIONp and TIOHp.
This in turn means that- as regards D c , the latter cannot be either Rp or
Spj it must be Rp, a conclusion which is corroborated by the fact that
ZD C (=ERp)' and DZc (=REp) occur 9 times each. Thus far, then, the iden-
tifications, when inserted in an enciphering alphabet, are 'as follows:
Plain ABCDEFGHIJKLMNOPQRSTUVWXYZ
Cipher S Z V TH DGFI
F G
46, Substituting deduced values in the cryptogram . — a. Thus far the
analysis has been almost purely hypothetical, for as yet not a single one
of the values deduced from the foregoing analysis has been tried out in
the cryptogram. It is high time that this be done, because the final
test of the validity of the hypotheses, assumptions, and identifications
made in any cryptographic study is, after all, only this: do these hy-
potheses, assumptions, and identifications ultimately yield verifiable,
intelligible plain text when consistently applied to the cipher text?
b. At the present stage in the process, since there are at hand the
assumed values of bub 9 out of the 25 letters that appeal’, it is obvious
that a continuous ’'reading'* of the cryptogram can certainly not be expect-
ed from a mere insertion of the values of the 9 letters. However, the
substitution of these values should do two things. First, it should
immediately disclose the fragments, outlines, or "skeletons" of "good"
words in the textj and second, it should disclose no places in the text
where "impossible" sequences of letters are established. By the first
is meant that the partially deciphered text should show the outlines or
skeletons of words such as may be expected to be found in the communi-
pationj this will become quite clear in the next subparagraph. By the
second is meant that sequences, such as "AOOEN" or "TKRSEEO" or the like,
obviously not possible or. extremely unusual in normal English text, must
not result from the substitution of the tentative identifications result-
ing from the analysis. The appearance of several such extremely unusual
or impossible sequences would at once signify that one or more of the as-
sumed values is incorrect.
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90
REF ID: A5 68 95
c. Here are the results of substituting the nine values which have
been deduced by the reasoning based on a classification of the high-
frequency letters into vowels and consonants and the study of the members
of the two groups:
1 2 3 4 5 S 7 8 0 10 11 12 13 14 If 1C 17 18 19 20 21 22 23 24 25
10 1C 23 35 19 10 3 19 15 5 6 35 19 19 35 23 14 10 5 19 15 4 35 23 10
A SFLZFIOGHLPZFGZDYSPFHBZDS
ATRET SO ETSER A TO ERA
S S T ST S
19 10 15 22 19 5 S 5 10 23 10 10 14 18 3 18 19 10 15 22 19 8 23 35 35
B GVHTFUPLVDFGYVJVFVHTGADZZ
SIO'NT IRTS I ITIONS REE
T S ST ST
8 10 22 14 23 35 14 19 35 3 35 22 19 5 22 10 22 35 4 23 10 19 13 22 85
C AITYDZYFZJZTGPTVTZBDVFHTZ
N RE TE ENS NINE RITONE
ST S
23 19 3 10 4 19 10 23 33 14 10 22 8 3 10 14 10 22 3 19 10 2 19 36 35
D DFXSBGIDZYVTXOIYVTEFVMGZZ
RT A S RE IN IN TI SEE
ST ST
22 15 5 5 16 8 35 23 19 2 16 22 35 8 10 22 14 23 35 14 4 23 16 19 15
E thlLvxzdfmhtzaitydzybdvfh
NO I ERT ONE - N RE RITO
S S
22 35 23 19 2 36 23 36 ft 8 10 8 10 10 10 36 14 10 8 16 10 10 6 10 35
F tzdfkzdzzjsxisgzygavfslgz
nert eree a ase S ITA SE
S T T S T
23 22 15 15 22 1 23 35 2 19 10 22 14 35 23 3 35 19 19 15 22 35 8 10 22
G DTHHTCDZRSVTYZDOZFFHTZAIT
RNOON RE AIN ER ETTONE N
S S
24 23 35 14 19 8 15 23 19 35 35 22 2 16 10 22 14 35 14 10 23 35 19 16 5
H YDZYGAVDGZZTKHITYZYSDZGHU
RE S IRSEEN 0 N E ARESO
T T T
35 19 35 22 19 5 5 10 23 10 8 1 24 16 8 8 10 2 6 36 23 19 6 10 23
J ZFZTGUPGDIXWGHXASRUZDFUID
ETENS SR SO A ERT R
S T T T S
3 19 15 22 IS 3 8 19 8 8
K EGHTVEAGXX
S 0 N I ’ S
T T
91
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d. No impossible sequences are brought to light, and, moreover,
several long words, nearly complete, stand out in the text. Note the
following portions : A21
HBZDSGVHTP
(1) 0?ERASI0NT
T S
CIS
TVTZBDVPHTZDF
(2) NINE7RIT0NERT
S S
F22
SLGZDTHHT
(3) A7SERN00N
T
The words are obviously OPERATIONS, NINE PRISONERS, and AFTERNOON. The
value G c is clearly Tpj that of F c is Spj and the following additional
values are certain:
Bc=Pp L c =Fp
47, Completing the solution . — a. Each time an additional value is
obtained, substitution is at once made throughout the cryptogram. This
leads to the determination of further values, in an ever-widening circle,
until all the identifications are firmly and finally established, and
the message is completely solved. In this case the decipherment is as
follows :
1 2 3 4 S 0 7 8 9 10 11 12 13 14 16 10 17 18 IS 20 21 22 23 24 25
A
B
c
D
E
F
G
II
J
K
SFDZFIOGHLPZF
ASRESULTOFYES
GVHTFUPLVDFGY
TIONSBYFIRSTD
AITYDZYFZJZTG
HUNDREDSEVENT
DFXSBGIDZYVTX
RSCAPTHREDINC
THLLVXZDFMHTZ
N0FFICERSX0NE
TZDFKZDZZJSXI
NERSWEREEVACU
DTHHTCDZRSVTY
RNOONQREMAIND
YDZYGAVDGZZTK
DREDTHIRTEENW
ZFZTGUPGDIXWG
ESENTBYTRUCKT
EGHTVEAGXX
GT0N1GHTXX
GZDYSPFHBZDS
TERDAYSOPERA
VJVFVHTGADZZ
IVISIONTHREE
PTVTZBDVFHTZ
YNINEPRISONE
OIYVTEFVMGZZ
LUDINGSIXTEE
AITYDZYBDVFH
HUNDREDPRISO
SGZYGAVFSLGZ
ATEDTHISAFTE
ZDOZFFHTZAIT
ERLESSONEHUN
HITYZYSDZGHU
0UNDEDARET0B
HXASRUZDFUID
0CHAMBERS3UR
92
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REF ID : A56895
Message: AS RESULT OF YESTERDAYS OPERATIONS BY FIRST DIVISION THREE
HUNDRED SEVENTY NIKE PRISONERS CAPTURED INCLUDING SIXTEEN OFFICERS ONE
HUNDRED PRISONERS WERE EVACUATED THIS AFTERNOON REMAINDER LESS ONE HUN-
DRED THIRTEEN WOUNDED ARE TO BE SENT BY TRUCK TO CITAKBERSBURG TONIGHT
T), The solution should, as a rule, not "be considered complete until
an attempt has "been made to discover all the elements underlying the gen-
eral system and the specific key to a message. In this case, there is no
need to delve further into the general system, for it is merely one of
uniliteral substitution with a mixed cipher alphabet. It is necessary
or advisable, however, to reconstruct the c5.pher alphabet, because this
may give clues that later may become valuable *
£, Cipher alphabets should, as a rule, be reconstructed by the
cryptanalyst in the form of enciphering alphabets because they will then
usually be in the form in which the encipherer used them. This is impor-
tant for two reasons. First, if the sequence in the cipher component
gives evidence of system in its construction or if it yields clues point-
ing toward its derivation from a key word or a key phrase, this may often
corroborate the identifications already made and may lead directly to
additional identifications . A word or two of explanation is advisable
here. For example, refer to the skeletonized enciphering alphabet given
at the end of subpar. 4 5b:
Plain ABCDEFGHIJKLMNOPQRSTUVWXYZ
Cipher S Z V TH DGFI
F G
Suppose the cryptanalyst, looking at the sequence DGFI or DFGI in the
cipher component, suspects the presence of a keyword-mixed alphabet.
Then DFGI is certainly a more plausible sequence than DGFI. Examining
the skeleton cipher component more carefully, he notes that S • . . Z
would allow for insertion of three of the missing letters TJWXY, since the
letters T and V occur later, probably in the keyword itself; further, he
notes that the key word probably begins under Fp and ends in TH, making
it probable that the TH is followed by AB or BC, This would mean that
either P, Qp=A, B e or B, C c . Assuming that P, Qp=A, B c , he refers to the
frequency distribution and finds that the assumptions Pp=A c and Qp=B c are
not good; on the other hand, assuming that T, Qp=B, Cc, the frequency
distribution gives excellent corroboration. A trial of these values
would materially hasten solution because it is often the case in crypt-
analysis that if the value of a very low-frequency letter can be surely
established it will yield clues to other valp.es very quickly. Thus,
if Qp is definitely identified it almost invariably will identify Up, and
will give clues to the letter following the Up, since it must be a vowel .
In the case under discussion the identification P, QprB, Cc would have
turned out to be correct. For the foregoing reason an attempt should
always be made in the early stages of the analysis to determine, if
possible, the basis of construction or derivation of the cipher alphabet;
as a rule this can be done only by means of the enciphering alphabet, and
93
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REF ID : A56895
not the deciphering alphabet# For example, the skeletonized deciphering
alphabet corresponding to the enciphering alphabet directly above is as
follows :
Cipher ABCDEFGHIJKLMNOPQRSTUVWXYZ
Plain R T S 0 U AN I E
S T
Here no evidences of a keyword-mixed alphabet are seen at all. However,
if the enciphering alphabet has been examined and shows no evidences of
systematic construction, the deciphering alphabet should then be examined
with this in view, because occasionally it is the deciphering alphabet
which shows the presence of a key or keying element, or which has been
systematically derived from a word or phrase. The second reason why it is
important to try to discover the basis of construction or derivation of
the cipher alphabet is that it affords clues to the general type of key
words or keying elements employed by the enemy. This is a psychological
factor, of course, and may be of assistance in subsequent studies of fyis
traffic. It merely gives a clue to the general type of thinking indulged
in by certain of his cryptographers .
d. In the case of the foregoing solution, the complete enciphering
alphabet is found to be as follows:
Plain ABCDEFGHIJKLMNOPQRSTUVWXYZ
Cipher SUXYELEAVNW ORTHBCDFGIJKMP
Obviously, the letter Q, which is the only letter not appearing in the
cryptogram, should follow P in the cipher component. Note now that the
latter is based upon the keyword IEAVENWORTH, and that this particular
cipher alphabet lias been composed by shifting the mixed sequence based
upon this keyword five intervals to the right so that the key for the
message is Ap=S c . Note also that the deciphering alphabet fails to give
any evidence of keyword construction based upon the word LEAVENWORTH.
Cipher ABCDEFGHIJKLMNOPQRSTUVWXYZ
Plain HPQRGSTOUVWFXJLYZMANBIKCDE
e. If neither the enciphering nor the deciphering alphabet exhibits
characteristics which give indication of derivation from a key word hy
some form of mixing or disarrangement, the use of such a key word for
this purpose is nevertheless not finally excluded as a possibility. For
the reconstruction of such mixed alphabets the cryptanalyst must use
ingenuity and a knowledge of the more common methods of suppressing the
appearance of key words in the mixed alphabets . Several of these methods
are given detailed treatment in par. 51 below.
f. It is very important in practical cryptanalytic work to pre-
pare a technical summary of the solution of a system. Step-by-step
® It is usual practice to employ as the specific key the equivalent
of either A-n, or the equivalent of the first letter of the plain compo-
nent when this component is a mixed sequence.
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94
REF ID: A56895
commentaries should accompany an initial solution; the steps taken should
he jotted down as they are made , and at the end they should he combined
into a complete resume of the analysis. The r€sum€ should he brief and
concise, yet comprehensive enough that at any future time the solution
may he reconstructed following the exact manner in which it was origi-
nally accomplished. Assumptions of words, etc,, should he referred to
with work sheet line- and column- indicators, and should he couched in the
proper cryptologic language or symbols, A short exposition of the mech-
anics of the general system, enciphering alphabets, enciphering diagrams,
etc,, as well as all key words (together with their derivation) and spe-
cific keys should he included. On the work sheet there should be a
letter-for-letter decryptment under the cipher text; the final plaintext
version should he in word lengths, with any errors or garbles corrected.
Hulls or indicators showing sentence separation, change of key, etc . , may
he enclosed in parentheses. All work sheets and notes should he kept
together with the solution.
48, General remarks on the foregoing solution .— a. The example
solved above is admittedly a more or less artificial illustration of the
steps in analysis, made so in order to demonstrate general principles.
It was easy to solve because the frequencies of the various cipher let-
ters corresponded quite well with the normal or expected frequencies.
However, all cryptograms of the same monoalphabet ical nature can he
solved along the same general lines, after a certain amount of experi-
mentation, depending upon the length of the cryptogram, and the skill
and experience of the cryptanalyst .9
h. It is no cause for discouragement if the N student 's initial
attempts to solve a cryptogram of this type require much more time and
effort than were apparently required in solving the foregoing purely
illustrative example . It is indeed rarely the case that every assumption
made by the cryptanalyst proves in the end to have been collect; more
often it is the case that a good many of his initial assumptions are in-
correct, and that he loses much time in casting out the erroneous ones.
The speed and facility with which this elimination process is conducted
is in many cases ‘all that distinguishes the expert from the novice.
a
The use of monoalphabetic substitution in modern military operations
is exceedingly rare because of the simplicity of solution. However, such
cases have occurred, and one rather illuminating instance may he cited.
In an important communication on 5 August 1918, General Kress von
Kressenstein used a single mixed alphabet, and the intercepted radio mes-
sage was solved at American GHQ very speedily. A day later another mes-
sage, but In a very much more difficult cipher system, was intercepted
and solved. When translated, it read as follows:
"GHQ Kress:
The cipher prepared by General von Kress was at once solved here.
Its further use and employment is forbidden.
Chief Signal Officer, Berlin. 11
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95
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REF ID: A5 68 95
c. Nor will tlae student always find that the initial classification
into vowels and consonants can he accomplished as easily and quickly as
was apparently the case in the illustrative example. The principles in-
dicated are very general in their nature and applicability, and there are,
in addition, some other principles that may he brought to hear in case of
difficulty. Of these, perhaps the most useful are the following!
(1) In normal English it is unusual to find more than two consonants
in succession, each of high frequency. If in a cryptogram a succession
of three or four letters of high-frequency appear in succession, it is
practically certain that at' least one of these represents a vowel.-*-®
(2) Successions of three vowels are rather unusual in English.
Fractically the only time this happens is when a word ends in two vowels
and the next word begins with a vowel.
(3) When two letters already classified as vowel-equivalents are
separated by a sequence of six or more letters, it is either the case
that one of the supposed vowel-equivalents is incorrect, or else that
one or more of the intermediate letters is a vowel -equivalent .-*-3
(4) Reference to Table 7-B of Appendix 2 discloses the following!
Distribution of first 18 digraphs forming 2? percent of English text
Number of consonant-consonant digraphs — ----------------- 4
Number of consonant-vowel digraphs — . — - 6
Number of vowel-consonant digraphs- — — — — — — 8
Number of vowel-vowel digraphs - 0
Distribution of first 53 digraphs forming j?0 percent of English text
Number of consonant-consonant digraphs ‘ — ' 8
Number of consonant-vowel digraphs—————————— 23
Number of vowel -consonant digraphs— — 18
Number of vowel-vowel digraphs— ————————————— 4
-*-® Sequences of seven consonants are not impossible, however, as in
STR ENGTH THRO UGH.
•*•-*- Note that the word RA DIOED , past tense of the verb RADIO, is coming
into usage.
A sequence of seven vowels is not impossible, however, as in THE
WAY YOU EARN.
13
Some cryptanalysts place a good deal of emphasis upon this principle as a method of locating the remaining
vowels after the first two or three have been located. They recommend that the latter be underlined throughout
the text and then all sequences of five or more letters showing no underlines be studied attentively. Certain
letters which occur in several such sequences are sure to bo vowels. An arithmetical aid in the study is as follows:
Take a letter thought to be a good possibility os the cipher equivalent of a vowel (hereafter termed a possible
vowel-equivalent) and find the length of each interval from the possible vowel-equivalent to the next known (fairly
surely determined) vowel-equivalent. Multiply the interval by the number of times this interval is found. Add
the products and divide by the total number of intervals considered. This will give the mean interval for that
possible vowel-equivalent. Do the same for all the other possible vowel-equivalents. The one for which the
mean is the greatest is most probably a vowel-equivalent. Underline this letter throughout the text and repeat
the process for locating additional vowel-equivalents, if any remain to be located.
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The latter tabulation shows that of the first 53 digraphs which form 50
percent of English text, 4l of them, that is, over 75 percent, are com-
binations of a vowel with a consonant. In short. In normal English the
vpwels and the high-frequency consonants are in the long run distributed
fairly evenly and regularly throughout the text.
(5) As a rule, repetitions of trigraphs in the cipher text are com-
posed of high-frequency letters forming high-frequency combinations. The
latter practically always* contain at least one vowel; in fact, if refer-
ence is made to Table 10-A of Appendix 2 it will be noted that 36 of the
56 trigraphs having a frequency of 100 or more contain one vowel, 17 of
them conbain two vowels, and only three of them contain no vowel. In the
case of tetragraph repetitions, Table 11-A of Appendix 2 shows that no
tetragraph listed therein fails to contain at least ‘one vowel; 27 of them
contain one vowel, 25 contain two vowels, and 2 contain three vowels*
(6) 'Quite frequently when two known vowel-equivalents are separated
by six or more letters none of which seems to be of sufficiently high
frequency to represent one of the vowels A E I 0, the chances are good
that the cipher-equivalent of the vowel U or Y is present.
d. To recapitulate the general principles, vowels may then be dis-
tinguished from consonants in that they are usually represented bys
(1) high-frequency letters;
(2) high-frequency letters which do not readily contact each other;
9 • 1 ^ ’
(3) high-frequency letters which have a great variety of contact;
(4) high-frequency letters which have an affinity for low-froquency
letters (i.e., low-frequency plaintext consonants) .
e. In the foregoing example the amount of experimentation or “cut-
ting and fitting" was practically nil, (This is not true <?f real cases
as a rule.) Where such experimentation is necessary, the underscoring of
all repetitions of several letters is very essential, as it calls attent-
ion to peculiarities of structure that often yield clues.
f . After a few basic assumptions of values have been made, if short
words or skeletons of words do not become manifest, it is necessary to
make further assumptions for unidentified letters. This is accomplished
most often by assuming a word.}**' Now there are two places in every mes-
sage which lend themselves more readily to successful attack by the assump-
tion of words than do any other places — the very beginning and the very
, end of the message. The reason is quite obvious, for although words may
begin or end with almost any letter of the alphabet," they usually begin
This process does not involve anything more mysterious than ordinary, logical reasoning,* there is nothing
of the subnormal or supernormal about it. If cryptanalytic success seems to require processes akin to those of
, medieval magic, if “hocus-pocus’ 9 is much to the fore, the student should begin to look for items that the claimant
• of such success has carefully hidden from yiew, for the mystification of the uninitiated. If the student were to
adopt as his personal motto for all his cryptanalytic ventures the quotation (from Tennyson’s poem Columbus)
appearing on the back of the title page of this text, he will frequently find “short cuts” to his destination and wiif
not too often be led astrayl
t
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and end with hut ft few very common digraphs pjp$ trigraphs . Very often
the association of letters in peculiar combinations will enable the stud-
ent to note where one word ends and the next begins. For example suppose,
E, If, S, ancL T have been definitely identified, and a sequence like the
following Is found in a cryptograms
' • • i E KT 8 HE . • •
Obviously the break between, two words should fall either after the S of >
E H T S or after the T of E If T, so that two possibilities are offered:
. . .EHTS/EE . . ., or. . .ENT/SNE. ; .. Since in
English there are very few words with the initial trigraph S N E, it is »
most likely that the proper division is •••ENTS/HE.... Of
course, when several word divisions have .been found, the solution is
more readily achieved because of the greater ease with which assumptions
of additional new values may be made.
g. Although a considerable amount of detailed treatment has been
devoted to vowel-consonant analysis, it is felt advisable again to caution
the student against the natural tendency to accept without question the
results of any one cryptanalytic technique exclusively, even one such as
vowel -consonant analysis which seems quite scientific in character.
^9. The probable-word 11 method; its value and applicability .— a. In
practically all cryptanalytic studies, short cuts can often be made by
assuming the presence of certain words in the message under study. Some
writers attach so much value to this kind of an "attack from the rear"
that they practically elevate it to the position of a method and call it
the "intuitive method" or the "probable-word method." It is, of course,
merely a refinement of what in everyday language is called "assuming" or
"guessing" a word in the message. The value of making a "good guess" can
hardly be overestimated, and the cryptanalyst should never feel that he
is accomplishing a solution by an illegitimate subterfuge when he has
made a fortunate guess leading to solution. A correct assumption a3 to
plain text will often save hours or days of labor, and sometimes there
is no alternative but to try to "guess a word", for occasionally a system
is encountered the solution of which is absolutely dependent upon this
artifice .
b. The expression "good guess" is used advisedly. For it is "good"
in two respects. First, the cryptanalyst must use care in making his
assumptions as to plaintext words . In this he must be guided by extra- *
neous circumstances leading to the assumption of probable words — not just
any words that come to his mind. Therefore he must use Tais imagination
but he must nevertheless carefully control it by the exercise of good
judgement. Second, only if the "guess" is correct and leads to solution,
or at least puts him on the road to solution, it is a good guess. But,
while realizing the usefulness and the time and labor-saving features of
a solution by assuming 'a probable word, the cryptanalyst should exercise
discretion in regard to how long he may continue in his efforts with this
method. Sometimes he may actually waste. time by adhering to the method
too long, if straightforward, methodical analysis trill yield results wore
quickly.
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£. Obviously, the "probable-word" method has much more applicability
when working upon material, the general nature of which is known, than when
working upon moi'e or loss isolated communications exchanged between corres-
pondents concerning whom or whose activities nothing is known. For in the
latter case there is little or nothing that the imagination can seize upon
as a background or bos is for the assumptions nowever, in the case of
military cryptanalysis in time of aotivo operations there is, indeed, so
great a probability that certain words and expressions are present in cer-
tain cryptograms that those words and expressions ("cliches") are often
referred to as "cribs" (as defined in Webster’s New Collegiate Diction-
ary: "...a plagiarism; hence, a translation, etc., to aid a student in
reciting."). The cryptanalyst is quite sure they are present in the
cryptogram under examination— what he must do is to "fit" the crib to
the text", that is, locate it in the cipher text.
d. Very frequently, the choice of probable words is aided or limit-
ed by" the number and positions of repeated letters * These repetitions
may be patent — that is, externally visible in the cryptographic text as
it originally stands— or they may be latent '— that is, externally invis-
ible but susceptible of being made patent as a result of the analysis.
For example, in a monoalphabetle substitution cipher, such as that dis-
cussed in the preceding paragraph, the repeated letters are directly
exhibited in the cryptogram; later the student will encounter many cases
in which the repetitions are latent, but are made patent by the analyt-
ical process. When the repetitions are patent, then the pattern or for -
mula to which the repeated letters conform is of direct use in assuming
plaintext words; and when the text is in word-lengths, the pattern is
obviously of even greater assistance. Suppose the cryptanalyst is deal-
ing with military text, in which case he may expect such words as DIVIS-
ION, BATTALION, etc., to be present in the text. The positions of the
repeated letter I in DIVISION, of the reversible digraph AT, TA in BAT-
TALION, and so on, constitute for the experienced cryptanalyst tell-tale
indications of the presence of these words, even when the text is not
divided up into its original word lengths.
e. The important aid that a study of word patterns can afford in
cryptanalysis warrants the use of definite terminology and the establish-
ment of certain data having a bearing thereon. The phenomenon herein
under discussion, namely, that many words are of such construction as
regards the number and positions of repeated letters as to make them
readily identifiable, will be termed idiomorphism (from the Greek ,, idios"»
one’s own, individual, peculiar 4 * "morphe" =form) . Words which show this
phenomenon will be termed idiomorphic . It will be useful to deal with
the idiomorphlsms symbolically and systematically as described below.
15 ..
’ .General GIvierge In bis Court de Cryplographie (p. 121) says: “However, expert cryptanalysts often
employ such details as are cited above [in connection with assuming the presence of ‘probable words’], and tho
experience of tho years 1014 to 1918, to cite only those, prove that in practice one often has at his disposal ele-
ments of this nature, permitting assumptions much more audacious than those which served for the analysis
of the last example. The reader would therefore be wrong in imagining that such fortuitous dements are
encountered only in cryptographic works where the author deciphers a document that ho himself enciphered.
Cryptographic correspondence, if it is extensive, and if sufficiently numerous working data are at hand, often
furnishes elements so complete that an author would not dare use all of them in solving a problem for fear of
being accused of obvious exaggeration.”
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f . When dealing with cryptograms in which the word lengths are
determined or specifically shown, it is convenient to indicate their
lengths and their repeated letters in some easily recognized manner or
hy formulas , This is exemplified, in the ease of the word DIVISION, hy
the formula ABCBDBEF; in the case of the word BATTALION, hy the formula
ABCCBDEFG, If the cryptanalyst, during the course of his studies, makes
note of striking formulas he has encountered, with the words which fit
them, after some time he will have assembled a quite valuable body of
data* And after more or less complete iists of such formulas have been
established in some systematic arrangement, a rapid comparison of the
idiomorphs in a specific, cryptogram with those in his lists will be feas-
ible end will often lead to the assumption of the current word* Such
listB can be arranged according to word length, as shown herewith:
3/aba : DID, EVE, EYE, etc,
abb : ADD, ALL, ILL, OFF, etc*
4/abac : ARAB, AWAY, etc.
abbe : ALLY, BEEN, etc*
abca : AREA, BOMB, DEAD, etc.
abeb s ANON, CEDE, etc.
etc . etc .
g. When dealing with cryptographic text in which the lengths of the
words are not indicated or otherwise determinable, lists of the foregoing
nature are not so useful as lists in which the words (or ports of words)
are arranged according to the intervals between identical letters, in the
following manner:
1 Interval
-DiD-
-EvE-
-EyE-
dlvlsion
revision
etc*
2 Intervals
AbbAcy
ArAbiA
AblAtive
AboArd
-AciA-
etc.
3 Intervals
AbeyAnce
hAbitAble
lAborAtory
AbreAst
AbroAd
etc . •
Repeated digraphs
COCOa *
-dERER
ICICle
-ININg
bAGgAGe
etc.
h. The most usual practice, however, in designating idiomorphic
patterns and classifying them into systematic lists is to assign a lit-
eral nomenclature to that portion of a word (or sequence of plaintext
letters) which contains the distinctive pattern, beginning with the first
letter which is repeated in the pattern and ending with the last letter
which is repeated in the pattern. Thus, the word DIVISION would he term-
ed as an idiomorph of the abaca class (based on the sequence 17131 con-
tained therein), and t he wor d BATTALION as an idiomorph of the abba class
(based on the sequence ATTA) * In Appendix 3 will he found a compendium
of the more frequent military words in English, arranged according to
word-lengths in alphabetical order and in rhyming order; in addition,
there will he found in this appendix a listing of idiomorphs arranged
first according to pattern and then according to the first letter of the
idiomorphic sequence.
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50, Solution of additional cryptograms produced lay the same compon -
ents «— -a. To return, after a rather long digression, to the cryptogram
solved in pars, 44 - 47, once the components of a cipher alphabet have
been reconstructed, subsequent messages which have been enciphered by
means of the same components may be solved very readily, and without re**
course to the principles of frequency, or application of the probable-
word method. It has been seen that the illustrative cryptogram treated
in paragraphs 4l - 47 was enciphered by Juxtaposing the cipher component
against the normal sequence so that A p =S c , It is obvious that the cipher
component may be set against the plain component at any one of 26 differ-
ent points of coincidence, each yielding a different cipher alphabet.
After the components have been reconstructed, however, they become
known sequences and the method of converting the cipher letters into
their plain-component equivalents and then completing the plain-component
sequence^ begun by each equivalent can be applied to solve any crypto-
gram which has been enciphered by these components •
b. An example will serve to make the process clear. Suppose the
following" message, passing between the same two stations as before, was
intercepted shortly after the first message had been solved:
IYEWK CEEHK OPOSE LFOOH EAZXX
It is assumed that the same components were used, but with a different
key letter. First the initial two groups are converted into their
plain-component equivalents by setting the cipher component against the
plain component at *any arbitrary point of coincidence. The initial let-
ter of the former may as well be set against A of the latter, with the
following result :
Plain ABCDEFGHIJKLMNOPQRSTUVWXYZ
Cipher LEAVNWORTHBCDFGIJKMPQSUXYZ
Cryptogram IYEWK CERNW
Equivalents— PYBFR LBHEF ...
The plain component sequence initiated by each of these conversion equiv-
alents is now completed, with the results shown in Fig. 15. Note the
plaintext generatrix, CLOSEYOURS, which manifests itself without further
analysis * The rest of the message may be read either by continuing the
same process, or, what is even more simple, the key letter of the message
pay now be determined quite readily and the message deciphered by its
means.
It must be noted that if the plain component is a mixed sequence^
then it is this mixed sequence which must be used to complete the
columns ,
i
- HEaTlUCTEP
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REF ID: A5 68 95
•R ESTRICTED
IYEWKCERKW
PYBFRLBHEF
QZCGSMCIFG
RADHTNDJGH
SBEIUOEKHI
TCFJVPFLIJ
UDGKWQGMJK
VEHLXRHNKL
WFIMYSIOLM
XGJNZTJPMN
YHKOAUKQWO
ZILPBVLROP
AJMQCWMSPQ’
BKNRDXNTQR
*C LOSEYOUR8 *
■ DMPTFZPVSI
ENQUGAQWTU
FORVHBRXUV
GPSWICSYVW
HQTXJDTZWX
IRUYKEUAXY
JSVZLFVBYZ
KTWAHGWCZA
LUXBNHXDAB
MVYCOIYEBC
NWZDPJZFCD
OXAEQKAGDE
Figure 15.
c t In order that the student may understand without question just
what is involved in the latter step, that is, discovering the key letter
after the first two or three groups have been, deciphered by the conver-
sion-completion process, the foregoing example will be used. It was
noted that the first cipher group was finally deciphered as follows t
Cipher—- I Y E W K
, Plain CLOSE
Now set the cipher component against the normal sequence so that Cp=I c ,
Thus:
Plain ABCDEFGHIJKLMNOPQRSTUVWXYZ
Cipher FGIJKMPQSUXYZLEAVNWORTHBCD
It is seen here that when Cp=I c then Ap=F c . This is the key for the en-
tire message. The decipherment may be completed by direct reference to
the cipher alphabet. Thus:
Cipher— IYEWK CERNW OFOSE LFOOH EAZXX
Plain CLOSE YOURS TATIO NATTW OPM XX
Message: CLOSE YOUR STATION AT TWO PM
nnnmnmmnrv
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d. . The student should make sure that he understands the fundamental
principles involved in this quick solution, for they are among the most
important principles in cryptanalytics * How useful they are will "become
clear as he progresses into more and more complex cryptanalytic studies*
e. It must be kept in mind that there are four ways v that two basic
sequences maybe used to form a cipher alphabet, subject "to the instruc-
tions guiding the cryptographer in- the use of his cryptosystem; this fact
must be considered when additional cryptograms appear in a particular
cryptosystem for which the primary components have been recovered* Assum-
ing that the sequences just recovered are labelled "A” and "B" , then the
following contingencies might arise in the encryption of subsequent mes-
sages:
(1) "A" direct for the plain component, and n B" direct for the
cipher component (as in the original recovery);
( 2 ) "A" direct for the plain, and "B” reversed for the cipher;
(3) "B" direct for the plain, and "A" direct for the cipher; and
(4) "B" direct for the plain, and "A” reversed for the cipher*
51* Derivation of key words ,— a* Concurrent with the solution of a
cryptogram, there should be a simultaneous effort in the reconstruction
of cipher alphabets and recovery of key words * Much labor can thus be
saved as recovery of the keys early in the stages of solution may trans-
form the process of cryptanalysis into one of decipherment.
b, A mixed cipher alphabet falls into one of five categories,
according to the composition of its components, viz .,
(1) the plain component is the normal sequence and the cipher com-
ponent is mixed;
(2) the cipher component is the normal sequence and the plain com-
ponent is mixed;
(3) both components are the same mixed sequence;
(4) both components are the same mixed sequence, but running in
reverse; or
(5) the components are different mixed sequences.
c, Let us examine several types of mixed sequences, using the key
word HYDRAULIC as an example. The ordinary keyword-mixed sequence pro-
duced from this key word is:
(1) HYDRAULICBEFGJKMHQPQSTVWXZ
itHOTRtCTED-
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REF ID: A5 68 95
The two principal transposition-mixed types "based on this key word are
derived from the diagram*
1 Y D R A U L I C
BEFGJKMKO ' .
PQSTVWXZ and read*
(2) HBPYEQDFSRGTAJVUKWL' MXINZCO and
(3) AJVCODFSHBPINZLMXRGTUKWYEQ
Other types may arise from variojis types of route transpositions such as
the following, using the foregoing diagram:
(4)
H
B
P
Q
E
Y
D
F
S
T
G
R
A
J
V
W
K
u
L
M
X
Z
N
I
C
0
(5)
H
Y
B
P
E
D'
R
F
Q
S
G
A
U
J
T
V
K
L
I
M
w
X
N
C
0
z
(6)
P
B
Q
H
E
S
Y
F
T
D
G
V
R
J
W
A
K
X
u
M
z
L
N
I
0
c
(7)
H
Y
D
R
A
U
L
I
C
0
U
M
K
J
G
y
E
B
p
Q
s
T
V
w
X
z
(8)
0
C
I
L
U
A
R
D
Y
H
B
P
Q
S
T
V
W«
X
z
N
M
K
J
G
y
E
(9)
H
Y
E
B
P
Q
S
T
G
F
D
R
A
U
K
j
y
W
X
Z
H
M
L
I
c
0
(10)
C
P
I
0
Q
B
L
N
S
E
H
U
M
z
T
y
Y
A
K
X
V
G
J)
R
j
w
Any transposition system may "be employed to produce a systematically-
mixed sequence; practicability of method is the only determining factor.
It must "be remembered that the greatest amount of systematic mixing will
produce a sequence inherently no more secure than a random-mixed alphabet,
d. The student would do well to construct "both enciphering and de-
ciphering versions of cipher alphabets recovered, as has "been previously
mentioned. For example, in the following case
Plain: JQNMFHLEBRSKGYZOTICDUVAWPX
Cipher: ABCDEFGHIJKLMNOPQRSTUVWXYZ
no semblance of a key is apparent; "but in the inverse form
Plain: ABCDEFGHIJKLMNOPQRSTUVWXYZ
Cipher: WISTHEMFRALGDCPYBJKQUVXZNO
the key-phrase "NOW IS THE TIME FOR ALL GOOD MEN TO COME TO THE AID OF
THEIR PARTY" 1 b quite clear. In other types of mixed sequences, first
the one form is attacked, and then if negative results are obtained the
inverse form is treated.
e. Let us consider the following cipher alphabet:
P: ABCDEFGHIJKLMHOPQRSTUVWXYZ
C: DWZMSOCRYATXBEFUGQHIVJKLNP
The section V W X seems to comprise superimposed parts of the non-keyword
J K L
portions of mixed sequences. Adding Y Z to the plain component, we get
REGTRICTEB
104
REF ID : A56895
t
*
L
1
DESTIUOTEB- i
V W X Y Z which is certainly consistent as far as alphabetical progres-
J K L N P
sion goes, and indicates that the letters M and 0 are present in the key
word of the cipher component. Continuing in this vein, the section
MNOQSTVWXYZis rapidly established by correlating both se-
BEFGHIJKLNP
quences • It is obvious that the plain component key word begins right
after the Z, and that the cipher component key word probably just pre-
cedes the B. Going to the right, Z R H suggests key words like RHOMBOID,
P Q R •
RHEUMATISM, etc. These trials are quickly repudiated } therefore we go on
to Z R E which is acceptable. Z R E K is found wanting, but Z R E P is
PQS PQST PQSU
very satisfactory, and this is soon expanded toZREPUBLIC, and in
PQSUVWXYZ
a moment or two we recover the complete cipher alphabet:
P: REPUBLICANDFGHJICMOQSTVWXYZ
C: Q S U V W X Y Z D E M 0 C R A T B F G H I J K L N P
f . In the example below the student will observe that the alphabets
are reciprocal: this is an indication of identical sequences at a shift
of 13, or that a mixed sequence running against itself in reverse has
been employed. In this case the W X Y Z points to the latter hypothesis.
Z Y X W
P: ABCDE'FGHIJKLMNOPQRSTUVWXYZ
C: HOJFTDHAKC IMLGBSUVPEQRZYXW
Starting with the V W X Y Z R cluster, we see that the key word begins
R Z Y X W V
with the letter Rj therefore the next letter should be a vowel. Z R A
W V H
is not acceptable, but Z R E is fine, showing that the letter U appears
W V T
in the key word. Continuing the same line of reasoning as in the preced-
ing example, and with a little further experimentation, the final alpha-
bet is discovered to be
P: REPUBLIC ANDPGHJKKOqSTVWXTZ
C: VTSQOMKJHGFDNAC ILBUPERZYXW
g. In the next example, all efforts to derive key words on the
basis of keyword-mixed sequences are fruitless: the conclusion is there-
fore drawn that this is a case of a transposition.
P: ABCDEFGHIJKLMNOPQRSTUVWXYZ
- C: ACSEJYIGWLFVMHXNKZPBQRDUTO
Considering the mechanics of the cryptography involved, and assuming for
the time being that Z is at the bottom of the matrix and not in the key
word, ye start with the letters to the left, or if this fails, to the
right' of Z in the cipher component, obtaining the column N which is not
' K
Z
incompatible if N is in the key word on the top row. If we place Y to
RE B TniCTEB -
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REF ID: A5 68 95
the left of Z and huild up Its column, we get E N which is excellent#
J K
Y Z
This is expanded into I ME K which quickly becomes 73.8^35269
GHJK P ARLIMENT
WXYZ BCDFGHJKO
QSUVWXYZ
This last example was very easy because none of the letters V W X Y Z ap-
peared in the key word; but other cases should hardly prove more difficult#
h# Two additional methods that have been encountered for deriving
mixed"" sequences maybe mentioned# One is a slight modification of the
preceding paragraph, when the key word contains repeated letters :
187 3' 4 9*526
COM, IT ,E ,
ABDFGHJKL
NPQRSUVWX
Y Z which produces the mixed sequence:
CAHYEKWFRIGSJVLXMDQOBPZTHU
The other method is an interrupted-key columnar transposition system:-^
513^26
V A L . E Y
B C)
D F G H I)
JKM)
N 0 P Q)
R)
6 T U W X Z) which produces the mixed sequence:
ACFKOTE IXLGMPUHQWVBDJKRSYZ
The first example will succumb to the treatment outlined in subpar. g,
whereas the second method is vulnerable owing' to the presence of the
fragments D J N, F K 0, and G M P in the sequence which may be anagram-
med# Note the fair-sized fragment B D J N R S, composed of an ascending
sequence of letters; this is an outward manifestation of the interrupted-
key columnar method#
i. There are still other methods used for the production of mixed
sequences, but space does not permit giving further examples# However,
the student should by this time be able to devise methods of attack for
any special cases that may present themselves, based upon the crypt-
analytically exploitable weaknesses or peculiarities inherent in the
system of cryptography involved.
17
It is to be noted that in this particular case the numerical key •
serves two purposes : (l) determining the cut-off point (and therefore
the number of letters) in each row of the diagram, after the appearance
of the keyword; and (2) determining the order of transcription of the
columns ,
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IS f^Arck \$S5
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REOTRIOTEB -
»■
TABLE OF'COMEEHTS
MILITARY CRYPTANALYSIS, PART I
Monoalphabetic Substitution Systems
Section Paragraphs Pages
I. Introductory remarks. . ... 1-3 1-10
- i
II. Basic cryptologic considerations 4-13 11-20
III. Fundamental cryptanalytic operations. 14-20 21-30
. - — . . y -
IV. Frequency distributions and their
fundamental uses 21-28 31-54
T
V. Unilateral substitution with standard
cipher alphabets............ 29-37 55-74
■*- -V 1 . i r-* * -
VI. Uniliteral substitution with mixed cipher
alphabets.... 1 ^ . 38-91 75-106
VII. Multiliteral substitution with s ingle -
equivalent cipher alphabets...... .......... 52-56 107-120
VIII. Multiliteral substitution with’ variants ....;.. 57-63 121-150
IX. Polygraphic substitution systems 64- 151-
X . Concluding remarks • • .........
APPENDICES
1. Glossary '
2. Letter frequency data - English
3. Word and pattern lists - En ;lish
4. Service terminology; stereotypes......
5. Letter frequency data - foreign languages
6. List of frequent words - English and foreign languages.
T . Cryptographic supplement
8. Lester S. Hill algebraic encipherment
9. Open codes and concealment systems
10 . Communication intelligence operations
11. Principles of communication security
12 . Bibliography; recommended reading
13. Problems - Military Cryptanalysis, Part I
14. Foreign language problems...
IMDEX
t *
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_ SECTION, VII “ . '
, JMULTILITERAL SUBSTITUTION WITH S INGLE -EQUIVALE1W CIPHER ALPHABETS
■ ■ -Paragraph
General types of multiliteral cipher alphabets * * - 52
The ; Baconian and Trithemlaa ciphers ...••*••• 53
Analysis of multiliteral, monoalphabetic substitution ciphers ...... .
Historically interesting examples 55
The _ international (Baudot) teleprinter code 5^
52. General types of multlllteral cipher alphabets .—a. $p#9a|L{!$i&r
betic substitution methods in general may be classified into
and multiliteral systems. In the former there is a strict M one-to-oja© w
correspondence between the length of the units of the plain and those of
the cipher text; that is / each letter of the plain text is replaced by a
single character in the cipher text. In the latter this correspondence
is no longer lp:lc but may be lp:2 c , where each letter of the plain > text
is replaced by a combination of two characters in the cipher text; or
3p*3 c > where a three -character combination in the cipher text represents
a single letter of the plain text, and so on. A cipher in which the cor-
respondence is of the lpSl c type is termed uniliteral in character; one
in which it is of the 3p:2 c type, biliteral ; lp:3 c , triliteral , and so on.
Ciphers in which one plaintext letter is represented by cipher characters
of two or more elements are classed as multiliteral.
b. Biliteral alphabets are usually composed of a set of 25 or 2 6
combinations of a limited number of characters taken in pairs. An
example of such an alphabet is the following: '
Plain- — —
--- A
B
C
D
E
F
G
H
I
J
K
L
M
Cipher
— ww
m
WI
WE
WE
HW
HH
HI
HP
HE
HE
IW
IH
Plain
— N
0
P
Q
R
S
T
U
V
W
X
Y
Z
Cipher-
— 11
IT*
IE
TW
TH
TI
TT
TE
EW
EH
El
EE
EE
This alphabet is derived from the cipher square or matrix shown in
Fig. l6. The cipher equivalent of each plaintext element is made up of
two coordinate letters from outside the cipher matrix, one letter being
the coordinate of the row, the other being the coordinate of the column
^ The terms unillteral and multiliteral, although originally applied
only to cipher text composed of letters, are used here in their broader
sense to enibrace cipher text in letters, digits, and even other symbols.
In more precise terminology, these terms would probably be monosynibolic
and polysymbolic, respectively, but the terms unillteral and multiliteral
are too well established in literature to be changed at this late time.
JflggTmC TEB-
107
REF ID: A5 68 95 - -
RIpSTOC r J?gD, . _
in which the plaintext letter is located* In other words, the letters at
the side and top of the matrix have heen used to designate, according to
t*>
WHITE
♦ ,' T - w
H
(1) I
« T
• • * E
- • ■ - Figure 1 6. ' -
a coordinate system, the cell occupied by each letter within the matrix*
The letters (or figures) constituting the coordinate elements of such
matrices are termed row and column indicators . '
c. If a message is enciphered by means of the foregoing biliteral
alphabet, the cryptogram is still monoalphabet ic in character. A fre-
quency distribution based upon pairs of letters will obviously have all
the characteristics of a simple, uniliteral distribution for a monoalpha-
betic substitution cipher. . . , ~ i
d. The cipher alphabets shown thus far in this text have involved
only letters, but alphabets in which the cipher component consists of
figures, or groups of figures, are not uncommon in military cryptography.^
Since there are but 10 digits it is obvious that, in order to represent
an alphabet of more than 10 characters by means of figure ciphers, combi-
nations of at least two digits are necessary. The simplest kind of such
an alphabet is that in which Ap=01, Bp=02, . . . Zps26j that is, one in
which the plaintext letters have as their equivalents two-digit numbers
indicating their positions In the normal alphabet. , ^
e . Instead of a simple alphabet of the preceding type, it is pos-
sible"" to use a diagram of the type shown in Fig. IT. In this cipher ■’* .
1
2
_2_
4
_5_
6
_x_
8
_2_
1
A
3
c
D
E
F
G.
H
i
j
2
K
L
M
N
0
P
Q
R
s
T
3
U
V
W
X
Y
Z
*
>
•
•
•
£
Figure 17.
’ ^ Although, as an extension of this idea, cipher alphabets employing
signs and symbols are possible, such alphabets are not suitable for
modern cryptography because they can be neither telegraphed nor tele-
phoned with any degree of accuracy, speed, or facility.
•A
B
C
D
E
F
G
H
I-J
K
L
M
N
0
P
Q
R
S
T
U
V
W
X
Y
Z
■ REF ID: A5 68 95
" « - - it . f |%
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the lettfer Ap Is represented "by the dinomg3 liy b_ By the dinome 12,
etc. Furthermore, this matrix includes provision 1 for the encipherment of
some of the frequently-used punctuation marks in addition to the 26 let-
ters. . . ' ' '
f . Other types of billteral cipher alphabets are illustrated in the
examples below; ' ‘
5
6
7
8
JL
go]
-
1
2
3
5
6
JL
8
9
1
A
B
C
D
E
"F
: 1
A
B
C D
E
F
G
H
I
2
G
H
I-J K
L
M
2
J
K
L M
N
0
P
Q
R
3
W
0
P
Q
R
S
3
S
T
U V
W
X
Y
z
*
k
T U-V W
X
Y
z
•
•‘Figure 19.
Figure l8a
•
-V« .’j-
-
-M
u
N
I
C
H
‘A
B
C D
E
F
G
H
I
B
G
7
E
5
R
M
. . a’
A
D
G J
M
P
S
V
Y
E
A
1
N
Y
B
2
B
B
E
H K
W
Q
T
W
Z
R
C
3
D
h
F
6
C
C
F
I L
0
R
U
X
1
I»
H
8
I
9
J
t\
D
2
3
4 5
6
7
8
9 0
I
IC
L
0
P
Q
s
R
T
U
V
W
X
z
Figure 21.
— - - » # . j.. i * \ !
Figure 20. ’ - v - -- --
£. It is to be noted that in alphabets of the foregoing types, the
row indicators maybe distinct from the column indicators (e.g., Fig. l8),
or they may not (e.g.. Fig. 19); of course, when there is any duplication
between the row and column indicators, it is necessary to agree beforehand
upon which indicator will" be given as the first half of the equivalent
for a letter, in order to avoid ambiguity, (in all of the systems de-
scribed in this and subsequent sections of this text, the row indicator
will always form the first part of an equivalent) . When letters are used
as row" and column Indicators they may form a key word (e.g.. Fig. 20), or
they may not (e.g.. Fig. 2l); the key words, if formed, may be identical
(e.g., Fig. l6) or different (e.g.. Fig. 20). Furthermore, the plaintext
letters maybe arranged within the matrix as a mixed sequence (e.g.. Fig.
20), either systematically- or random-mixed; and the matrix may contain,
in addition to the letters of the alphabet, punctuation symbols (Fig. 17),
numbers (Figs. 20, 2l), etc., permitting their enc ipherment as such, in-
stead of having to be spelled out.
3
A pair of digits is called a dinome ; similarly, a tr 3 nomo is a set
of three digits ; a tetranome , a set of four digits ; etc . Although a
single digit would properly be termed a mononome, for the sake of euphony
it is shortened into the term monome.
REF ID: A5 68 95
h. When letters are vised ag £pv .and column Indicators, 'they may he
selected so as to result in producing cipher text that resembles arti-.
ficial words ; that is, words composed ,of alternate vowels and consonants.
For example, if in Figure 1 6 the row Indicators consisted of the vowels
A E I 0 U in this sequence from the top down, and the column indicators
consisted of the consonants B C D' F G in this Sequeftcd' from left to right,
the word RAIDS would he enciphered as OCABE FAFOD, which very closely
resembles code of the type formerly called artificial code language.
Such a system may he called a false , or pseudo -dodo" system.
i. As a weak type of subterfuge, hllitera! ciphers "may involve a
third"*character appended to the basic two -character cipher unit; this is
done to "camouflage” the biliteral nature of the cipher texb. This "third
character may he produced through the "use of a cipher matrix of the type
Illustrated in Fig. 22 (wherein Ap»6ll, Bp=6l2, etc.); or the third char-
acter may he a "sum-checking" digit which is the non-carrying sum (l.e.,
the sum modulo 10)5 of the preceding two digits, such as in the trinomes
257, 831, end 662 } or it may merely he a randomly-selected character .(in-
serted solely for the purpose of Reading the cryptanalyst astray).
- i » *■ + * ,J
-1 2 3 4 5
61
A
B
a
D
72
F
G
HI-JK
83
L
M
K
0
P
94
Q
R
S
T
U
05
V
W
X
Y
Z
Figure 22.
. > ' ' . ' ' » - T. •• :‘-pZ *5; A »r r ,• * '
. Another possibility that lends Itself to certain, multilateral
ciphers is the use of, a word spacer or word separator . This wprd.qepa-
rator might he represented by a value in the matrix; i *e . , "^theT separator
is enciphered (for instance, the diname " 39 ” in Fig. 19 might stand .for
a word separator) • The word separator miglit instead he a single element
not otherwise used in the cryptosystem; i.e,, unenciphered , and thus not
giving rise to any possible ambiguity. Thus, in Fig. the jligit 0 arid
in Fig. 21 the Vetter J might he. used as word separators, -since no con-
fusion would a„ Lie in decrypting. . . -
.Prior to 193*1-, international telegraph regulations .required codo. lA
words of five letters to contain at least one vowel .-and code words pf ten
letters to contain at least three vowels. The International Telegraph
Conference held in Madrid in 1932 amended these regulations "to permit the
use of 5-letter code groups containing any combination of letters. These
unrestricted code groups were authorized for use. after p l. January 193^ •
The term modulo (abbreviated mod ) pertains to r a cyclic" scale or
basis of arithmetic; thus, in the modulus of 7, the numbers 8 and 15 are
equivalent to 1, and 9 and 16 are equivalent to 2, etc*; or expressed
differently, 8 mod 7 is 1, 9 mod 7 is 2. In cryptology, many operations
are expressed mod 10 and mod 2 6.
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k. The biliteral alphabets yielded by the matrices of Figs'. 16-21
may also be termed bipartite , because the cipher units of these alphabets
may be divided into two separate parts whose functions are clearly de-
fined, viz ., row indicators end column indicators. As will be discussed
later, this bipartite nature of most biliteral alphabets produced from
.cipher matrices constitute one of the weaknesses of these alphabets which
make them recognizable as such to a cryptanalyst. However, it is possible
to employ a cipher matrix in a manner which will produce a billteral
alphabet not bipartite in character. For example, using the matrix of
Fig. 23 one could produce the following billteral cipher alphabet in
- •' 09
15
■ 21
~ ' 27
’ - 33
' - Figure 23 • '
which the equivalent for any letter in the matrix Is the pujft
coordinates which indicate its cell in the matrix?
Plain —
A
B
c
D
£
F
G
g
I
«T
n
h
M
Cipher—
l4
20
19
12
22
23
24
10
17.
£6
Plain —
N
0
p
Q
R
S
T
u
V
w
25
Y
Z
Cipher —
29
30
31
13
32
34
16
35
36
37
11
38
* . — 1
. - 7
- :
• ’
l .»
.C-.
‘ i •
„ “ ’
The cipher units of this' alphabet are”, of course, biliteral $ but they are
not bipartite. Note the equivalent of A_, that is l4— if divided, it
yields the digits 1 and 4 which have no meaning per se : plaintext letters
whose cipher equivalents begin with 1 may be found in two different rows
of the matrix, and those whose equivalents end in 4 appear in three dif-
ferent columns. ...
1
2
3 *
5
H
Y
D R
A
U
L I-J C
B
E
F
G K
H
N
0
P Q
S
T
V
W X
z
53* The Baconian and Trithemian ciphers ,— a. An interesting example
in which the cipher equivalents are five-letter groups and yet «the re-
sulting cipher is strictly' monoalphabetic in character is found in the
cipher system invented by Sir Francis BacoxL (1561-2.626) over 300 years
ago . Despite its antiquity the system possesses certain features of
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- i#
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111
4
REF TD:A 56895
- REOTniCTED
merit which are well worth noting. 0 Bacon proposes the following 24-
element cipher alphabet, composed of permutations of two elements taken
five at a time:?
♦ „ ,
A=aaaaa
I-Jrabaaa
’ . R"baaaa
Bcaooab
ICrabaab •
Ssbaaab
Czaaaba
Lzababa"
. Tcbaaba
Dzaaabb
Mrababb
U-V zbaabb
Eraabaa
N-dbbaa
Wsbabaa
Fraabab
Ocabbab
Xrbabab
Gcaabba
Prabbba
, . Yrbabba
Hraabbb
Qcabbbb
Zrbabbb
If this were all there were to Bacon’s invention it would he hardly worth
bringing to attention. But what he pointed out, with great clarity and
simple examples, was how such an alphabet might be used to convey a
secret message by enfolding it in on innocent, external message which
might easily evade the strictest kind of censorship. As a very crude
example, suppose that a message is written in capital and lower-case let-
ters, any capital letter standing for an "a" element of the cipher alpha-
bet, and any small letter, for a "b" element. Then the external sentence
"All is well with me today' can be made to contain the secret message
"Help." Thus:
A L 1 is
t a a b b b.
v -
H
WEIL
a a b a
' v —
E
W I t H m E
a, ,a b a b a.
>_/ N — -y» — '
L
Today
a b -b b a '
>
P
Instead of employing a device so obvious as capital and small letters,
suppose that an "a" element be indicated by a very slight shading, or a
° For a true picture of this cipher, the explanation "of which is often
distorted beyond recognition even by cryptographers, see Bacon’s own des-
cription of it as contained in his De Augmentls Scientiarum- (The Advance -
ment of Learnin g), as translated by any first class editor, such as Gilbert
Watts (l64o) or j'lilis , Spedding, and Heath (l857, 1870). The student Is
cautioned, however, not to accept as true any alleged "decipherments" ob-
tained by the application nf Baeoh's cipher to literary works of the 16th
century. These readings are purely subjective.’
7 1 .■ '
Bacon’s alphabet was called by him a "bilitteral alphabet" because it
employs permutations yf two letters . But -from the cryptanalytlc stand-
point the significant, point is that each plaintext letter is represented
by a 5-character equivalent. Hence, present terminology requires that
this alphabet be referred to as a ouinqueliteral alphabet . Although the
quinqueliteral alphabet affords 32* permutations. Bacon used only 24 of
them, because in the l6th century the letters I and J, U and V were used
interchangeably. Koto the regularity of construction qf .Bacon’s bilitcral
alphabet, a feature which easily permits its reconstruction from memory.
112
' ■ ■ - ‘REE* ' I-D : A568-95
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RESTRICTED . ..
• » - - * - - ...
very slightly heavier stroke • Then a secret message might easily he thus
enfolded within an external message of exactly opposite meaning. The
number of possible variations of this basic scheme is very high. The
fact that the characters of the cryptographic text are bidden in some
manner or other has, however, no effect upon the strict monoalphabetlcity
of the scheme.
b. Almost 100 years before Bacon’s time, the abbot Trithemlus,
born Johann von Heydenberg ( l462-151<j), Invented a‘ triliteral alphabet
which he evidently intended to use in a fashion similar to Bacon’s
alphabet; i.e., as a means of disguise or cov er for a secret text. This
alphabet, modified to include the 2 6 letters of the present-day English
alphabet, is shown in Fig. 23 below; it consists of all tke permutations
of three things taken three at a time, i.e., 3^ or 27 in all.
A=lll
D=121
G=131 ’
J=211
M=221
P=23l
s=31i “
v=32i
Y=331
B=112
£=122
H=132
K=212
11=222
Q=232
T=312
W=322
z=332
0=113
F=l23
1=133
L=213
t: -z-
' 0=223
« is U .
R=233
1 r 1 ^ a
'17=313
■X=323
#=333
•
■■ ■ T- "
- -- -} * t -=rr '
\y' \j.
- *T
'Figure 23.
. > 1 i. * J-- J , 9 « 4
' t’
I- -• p
' *
The cipher text of course does not have to be restricted to digits; any
groupings of three things taken three at a time will do. ‘
Analysis of multiliteral, monoalphabetic substitution ciphers . •
a. Biiiteral ciphers and those of the other mnltiliteral (trilateral ,
quadriliteral, . . .) types afeH&'ften readily detected externally by the
fact that the cryptographic text is usually composed of but a very limi-
ted number of different characters . They are handled in exactly the same
manner as are uniliteral, monoalphabetic substitution ciphers. So long
as the same’ character, or combination of characters, is always used to
represent the same plaintext letter, and so long as a given letter of the
plain text is always represented by the same character or combination of
characters, the substitution is strictly monoalphabetic and can be handled
in the simple manner described in the preceding section of this text.
~i
b . In the case of biliteral ciphers in which the row and column, in-
dicators are not identical, and the direction of reading the cipher pairs
is chosen at will for each succeeding cipher pair, an analysis of the
contacts of the letters comprising the cipher pairs will disclose that
there are two distinct families of letters, and a cipher pair will never
consist of two letters of the same family. With this fact discovered,
the cipher may be quickly reduced to unlliteral terms and solved iu the
manner previously mentioned.
c. If a multiliteral cipher includes provision for the encipherment
of a word separator, the cipher equivalent of this word separator may be
readily identified because it will have the highest frequency of any ci-
pher unit. On the other hand, if the word separator is a single char-
acter (see subpar. 52j}. on the use of the digit 0 and the letter J), this
RE S TRICTED
113
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REF ID: A5 68 95
character may be identified throughout the encrypted text hy its position-
■ al appearance spaced "vordlength-vise*' in the cipher text, and by the
fact that it never contacts itself. If this single character is used as
a null indiscriminately throughout the cipher text, instead of. as a v$rd
separator, the analysis is a bit more complicated but not as great as
might be thought.
d. As a general rule, it is advisable to reduce multiliteral cipher
text to unillteral equivalents^ especially if a triliteral frequency dis-
tribution is to be made. w If not more" than .36 different combinations are
present in a cryptogram, the extra values over 26 maybe represented by
• digits for the purpose of this reduction. If, however, more than 36
different combinations are found in the encrypted text, it is usually not
worth the' trouble to attempt any uniliteral reduction, and the cipher
text can be attacked in its multiliteral groupings .
e# As one of the first steps in the solution of any multiliteral
cipher in letters which appears to Involve the use of a cipher matrix,
it is generally advisable to anagram the letters comprising the row ajad
column Indicators in an attempt to disclose any key words for these In-
dicators » 'When the anagramming process does disclose such a key word or
words, the next step is to make a skeleton reconstruction matrix which la
a duplicate of the original enciphering matrix in that the indicators are
arranged in the same order as on the original. Then, as plain text is
recovered in the cryptogram by any of the methods outlined in the previous
section of this text, the recovered plaintext letters should be Inserted
in the proper cells of the reconstruction matrix, so that any systematic
arrangement of the plaintext letters, if present in the original, may be
disclosed prior to recovery of the complete plain text. Furthermore, it
may in some instances be found worthwhile, immediately after successfully
uncovering the key words used as indicators, to make a frequency distri-
bution of the particular cryptogram In the form of tally marks within the
*• properly arranged frame of the reconstruction matrix, because it may be
that a few moments * study of the Ibcations of the crests and troughs in
the distribution made in that form may, if the plaintext letters are ar-
ranged in the normal sequence or in a keyword-mixed sequence (especially
if it is related to the keywords for tho indicators), provide a basis
for the derivation of this sequence at one stroke, without recourse to
analysis of W i cipher text.
55 * Historically interesting examples .— a. Two examples of multi -
literal ciphers of historical interest will be cited as Illustrations.
During the campaign for the presidential election of 1876 (Hayes vs.
Tilden) many cipher massages were exchanged between the Tilden managers
and their agents in several states where the voting was hotly "contested.
Two years Inter the Hew York Tribune® exposed many irregularities In the
1879
New York Tribune,
I ■
. 1
Extra No. Uk, The Cipher Dispatches, "New York,
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114
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REF ID: A5 6 8 95
campaign "by publishing the decipherments of niany of these messages
These decipherments were achieved hy two investigators Employed by the
Tribune, and the plain text of the messages'^ seems to’ show that illegal
attempts and measures to carry the election for Tilden' were made "by his
managers. Here is one of the messages: . .
JACKSONVILLE, Nov. 16 (1876).
GEO. F. RANEY, Tallahassee. t
Ppyyemnsnyyypimashnsyyapit'Spaadnshns
pensshnsmmpiyysnppyeaapielssyeshainsssp
eeiyyshnynsssyepiaanyitnsphyyspyypinsyy
ssitemeipimmeisseiyye is si t e ™i epyyp e e iaas s
imaayespnsyyiansssei s s'm in p pnspinssnpins in
imyyitemyysspeyy m'm nsyyssitspyypeepppma
a a y y p i i t
L' Engle goes up tomorrow. - “ . _
- *? DANIEL.
Examination of the message discloses that only ten different letters are
used. It is probable, therefore, that what one has here is a cipher
which employs a multiliteral alphabet. First assuming that the alphabet
is one in which combinations of two letters represent single letters of
the plain text, the message is rewritten in pairs and substitution of
arbitrary letters for the pairs is made, as seen below:
• ■ ■- Silt.f C* t MB V « t » i v ■ * r x
— A *
HP YY ’ EM NS NY YY PJ HA SH NS YY S3 «t0.
A B C.D E B F 0 5 D.B'I eto.
A triliteral frequency distribution .is then made and analysis of the mes-
sage along the lines illustrated in the preceding section of this text
yields solution, as follows:
Jacksonville ? Nov. l6.
GEO. F. RANEY, Tallahassee:
Have Marble and Coyle telegraph for influential men from Delaware and
Virginia. Indications of weakening here. Press advantage and watch
Board. L ’Engle goes up tomorrow.
DANIEL.
b. The other example, rising numbers, is as follows':
S. PASCO
and E.
M. L
’ENGIE:
-
84
55
84
25
93
34
82
31
93
20
93
66
77
66
33
84
52
48
44
55
42
82
48
89
-*■ . f f - r
Jacksonville, Nov, 17.
31.
~75
93
82
77
33'
55
42
66
.31
31
93
,20
82
33
66
42
93
31
82
66
75
ft
31
93
- dmiel/ *
RESTRICTED
115
. . REF. ID: A5 68 95 ,
RE S TRICTED - , / .
' * ^
There were, of course, several messages of like ija^ure, and examination
disclosed that only 2o different numbers in ail were'used. * Solution of
these_ ciphers followed v§pjr 'easily, the decipherment of the one given
above being as follows : ■
• * *' * “ * r T\i* •?*! , . r
Jacksonville, Nov. 17.
S. PASCO and E. M. L’BNGLE:
Cocke will be ignored, Eagan called in. Authority reliable •
DANIEL.
c , The Tribune experts gave the following alphabets as the result
of their decipherments:
AA«0
EN“Y
IT=D
NSrE
PP=H
SS=N
_
. ’i '
AI=U
EP=C
ma=b
NY=M
SH=L
YE=F
EI*I
IA*K
mzG
FE3
SN=P
YI=X
EM=V
B1«=S
NN=J
PI =B
SP=W
YY=A
20 =D
33=N
44=H
6 2=X
77=0
89=Y
*" ••"■»*» *■ »"
u ,
25=K
34=w
48:3
66 =A
82=1
93 =E ‘
* - - t «- ■ 1 - ■ - -
“■
27=s
39=P
52=U
68= F
84 =C
96 =M
■
3l=L
42=R
55=0
75=B
87=V
99=J
. 1 « t .»
- ■*
!•’* - 1J'
They did not attempt to correlate these alphabets, or at' least tfcey say
nothing about a possible relationship . The present author has, however,
reconstructed the rectangle upon which these alphabets are based, and It
is given below (Fig . 24) .
"2d Letter or Number
HI SPAYMENT
12 34567890
I REaTRICTED r ’ u 6
REF ID -: £56895
RESTRICTED
It is amusing to note that the conspirators selected a? their key a
phrase, quite in keeping with their attempted illegalities ~.HIS PAYMENT -
for bribery seems to hove played a considerable part in that campaign.
The blank cells in the matrix probably contained proper names, numbers,
etc .9 '
56 . The international (Baudot) teleprinter code . --a. Modem print-
ing telegraph systems,!^ or teleprinter systems as they" are more often
called, make use of a five -unit code-D- or alphabet which is similar to
the Baconian alphabet treated in par. 53* Like the Baconian alphabet,
the teleprinter alphabet is composed of permutations, .of two elements
taken five at a time, making it possible to, obtain 32 different permu-
tations, 2 6 of which are assigned to v bhe.l§$terq; of the. alphabet, leaving
1 for an "idle condition" and 5 for certain pointer operations called
functions, such as "space", "figure shift", "letter shift,." etc.
1 - - - 1 • $
. J ‘A ^
_ b. During electrical transmission, the two ^distinct elements of
which each character, is ,cgmpo?ed take _ the form, of (l) a timed interval of
electrical current and (2) a timed interval of no current, which are
commonly referred to as "mark" impulses and "space" impulses, respective-
ly. In certain operations, a paper tape is prepared of the traffic to be
transmitted, or a paper tape may be prepared of the incoming traffic at
the receiving end; in such tapes, the elements of the Baudot characters
take the form of punched holes ("mark" impulses ) and imperforate positions
("space" impulses; ... - -
.i — ,*
9
As was. mentioned in a previous footnote, a matrix containing such
items would be termed' a* syllabary Square; jor example of such matrices
see the treatment of syllabary squares and* code charts in Section X. ^
Such systems are characterised by the. transmission and reception-
printing of messages by electrical means, .incorporating two electrically-
connected instruments , resembling typewriters . .When a key of the keyboard
on the transmitting instrument is depressed, an electrical signal is
transmitted to the receiving instrument , causing the’ corresponding char-
acter to be printed therein. Usually the message is printed at the local
as well as the distant station. The system has been .adapted to radio as
well as wire and overseas cable transmission, _ ' _ •
The five -unit .code was first; applied, to teleprinter systems by Jean
Maurice Emile Baudot (1845-1903), and is commonly known as the Baudot
code . It is worthwhile to point out that Baudot apparently constructed
his alphabet to correspond' with normal frequencies, of characters (with
certain exceptions), since .the most frequent ones are represented by per-
mutations requiring the least electrical energy on the. basis of "marking"
and "spacing." In this respect Baudot "took, a leaf out of Morse's note-
1>00k< ” ' SWV ••
St’"**’'
y r i - - — "i * yt *
.■* ” - .
RESTRICTED.
117
- REE ID : A568 95
c. The teleprinter co$£ in international use is given in Chart 7 f
helowj wherein the mark and space impulses {known collectively as ’bauds )
are illustrated as the holes (shown as black dots) and ’’no-holes” of.
teleprinter tape. The letter equivalents (’’lower case”) are self-explan-
atory, The figure shift is used to change the meaning of a particular
character to an ''upper” case” equivalent, ‘and when it is desired to return
to lower case, the letter shift is used; in regular teleprinter ^usage.
WEATHER SYMBOLS
COMMUNICATIONS
DlBQOq
■UBUPIlHl
ui
□□□□□□I
■□gBSiBSB
Chart J, I^perhutfona}. telop^ntet code.
the " communications” set of upper -case equivalents are the ones recorded
on the typed copy by the teleprinter/ whereas' the ’’weather symbols” are
the upper-case equivalents whicfy are printed in teleprinter systems Re-
signed for the sendipg and receiving of weather, information. The spap^
is used to separate words? the .carriage, return (C.R.) effects the retupj}
of the teleprinter carriage to the right and the line feed (L.F.) rolls
the platen to the next line for printing (cf, the corresponding functions
of an ordinary typewriter) 1 In addition, when the upper-case equivalent
of ”S" is used, a bell rings in the receiving ‘ teleprinter ' as ^ a Signal to
call the operator to Mb machine, or to indicate that traffic is about' to
be sent. * , • • r y ’ ; '
- - 1 * *■ w* I Jf ■ 1+ 'f t , . I . * '
d. In Fig. 25 1 b shown a portion of, a teleprinter tape containing
the beginning of the phrase “New is the time for all- good men ...”
NOW IS THE TIME'; JfOTi ALL'.GOOti MEN "
Figure 25. - .
The small holes, one of which appears in every position of tiic tape be-
tween the second and third levels, dre sprocket holes used for advancing
the tape through the transmitter unit.
RESTRICTED
- REF- -ID": AS6B'B5
T ' V
u . .
■’k* £**'. .1# . —
V
e. It is to to emphasized that messages are not made secure from
unauthorized reading merely by sending them by means of an ordinary tele-
printer system- -the teleprinter alphabet is internationally known, just
as the English, Russian, etc. alphabets are. In order to provide secur-
ity for a teleprinter message, it is just as necessary to app]y thereto
some sort of cryptographic treatment as it is to any other kind of mes-
sage . The cryptosystems used for teleprinter t encryption may involve
either, or both, of the two classes of cryptographic treatment, viz*,
substitution and transposition. A substitution treatment "might involve
changing certain of the mark impulses of the characters comprising a mes-
sage to space impulses, and vice versa, according to a prearranged sys-
tem; a transposition treatment might involve changing the order of the 5
impulses in the Baudot equivalents for. the characters comprising a mes-
sage; and so on. The cryptographic treatment can be accomplished by a
special cipher attachment (called an " applique unit”) to a teleprinter;
thus ho modification of the teleprinter itself would be necessary. There
are, of course, self-contained cipher teleprinters designed as such for
engineering or cryptographic reasons, or both.
f . In the analysis of encrypted tele]?rinter systems, recourse is
had to special tables^ of the frequencies of single Baudot characters,
digraphs, trigraphs, etc., as they appear in teleprinter traffic. It is
:ic,
, as in any other type of
;or, this character has the ,
Furthermore, one of the
important to note that in teleprinter trafi
traffic involving the use of a word separa;
highest frequency of any plaintext element
highest-frequency plaintext digraphs, in addition to those wherein the
word separator constitutes one of the elements , will be the coitil lnation
"carriage-return/line-feed" , since this combination of characters is used
in the normal procedure of typing each line of text on the teleprinter.
In such tables, as is common in cryptanalytic practice, the mark im-
pulses are designated by a plus symbol ( + ), and the space impulses are
designated by a minus symbol ( - ) . In addition, it is usual in such
tables to denote the character representing the figure shift by the digit
"2”, the space by "3", the letter shift by "4” , the line feed by ”5”, the
blank by ”6" , and the carriage return by "7” •
RESTRICTED
REF ID: A5 68 95
REF ID:'A5 68 95
RESTRICTED
SECTION VIII
• * r '- . . ffe'MULTILITERAL SUBSTITUTION WITH VARIANTS
* t~- - ■' --
t ’* • — * j
' . ■ Paragraph
Purpose of providing variants in monoalphahetic substitution 57
Simple types of cipher alphabets with variants..* ' 58
More complicated types of cipher alphabets with variants............ 59
Analysis Of simple examples ...... t ' 60
Analysis of more complicated examples ....^. 6l
Analysis involving the use of isologs ;;.V. 6z
Further remarks on variant systems 63
-- ■» ■ r » ( *■ * „ ' r " * - ^ k ** i „ j* -
57 « ' Purpose of providing variants in monoalphahetic substitution . --
It has been seen that the individual letters composing ordinary
intelligible plain text are used with varying frequencies; some, such as
('in English) E, T, R, I, and N, are used much more often than others,
such as J, K, Q, X, : and Z. In fact, each letter has a characteristic
frequency which affords definite clues in the solution of simple mono-
alphabetic ciphers, such as those discussed in the preceding sections of
this text. In addition, the associations which individual letters form
in combining to make up words, and the peculiarities which certain of
them manifest in plain text, afford further direct clues by means of
which ordinary monoalphahetic substitution encipherments of such plain
text maybe more or less speedily solved. This has led cryptographers to
devise methods for disguising, suppressing, or eliminating the foregoing
characteristics manifested in cryptograms produced by the simpler methods
of monoalphahetic substitution. One category of such methods, the one to
be discussed in this section, is that in which the letters of the plain
component of a cipher alphabet are assigned two or more cipher equivalents,
which are called variant values (or, more simply, variants ) .
b . Basically, systems involving variants are multilateral^ and, in
such systems, because of the large number of equivalents made available
Uniliteral substitution with variants is also possible. Note the
following cipher alphabet, illustrated by Captain Roger Baudouin in his
excellent treatise, Elements de Cryptographie, p. 101 (Paris, 1939 ) -
Plain':
Cipher:
ABODE? GH I L MNOPQJR S TU V X Z
LGORFQAHCMBT
K X
V
IDNPUSYEWJ
Z
Baudouin proposed that Jp and Yp be replaced by 3 L; K_ by C or Q p ;
W-n by W-p — thus four cipher letters would be available as variants
d
and
for
e high-frequency plaintext letters in French.
-- .. —
RESTRICTED
121
RESTRICTED
REF ID: A5 68 95
i
"by the combinations and permutations of a limited number of elements, each
letter of the plain text may be represented by several multiliteral cipher
equivalents which may be selected at random. For example, if 3 -letter
combinations are employed as the multiliteral equivalents, there are
available 26’ or 17,57° such equivalents for the 26 letters of the plain
text; they may be assigned in equal numbers of different equivalents for
the 26 letters, in which case each letter would be representable by 676
different 3 -letter equivalents; or they may be assigned on some other
basis, for example, proportionately to the relative frequencies of plain-
text letters . For this reason this type of system may be moFe completely
described as a monoalphabetic, multiliteral [substitution with a multiple - ■
equivalent cipher alphabet *^ Some authors lerm such a, 'system 1 * simple ■
substitution with multiple equivalents"; otl ers term it ‘'monoalphabetic
substitution with variants", or multiliteraji substitution with variants .
For sake of .brevity and precise terminology, the latter designation will
be employed in this text, it being understood without - further restatement
that only such systems as are monoalphabetic will be discussed.
^ c. The primary object oi? monqalphabetic substitution' with variants
is t as has been mentioned t above, to provide several, Values which '.may be
eiiiployed at random in a simple substitution of cipher ^equivalents -foV'the
plaintext letters. ' . _ . . .... . , ,',t' ,.* 5 ^
t 1
d. A word or two concerning the underlying theory of (monoalphabetic)
multiliteral substitution with variants may not be amiss . ■ Whereas' iri
simple or single-equivalent substitution it has been seen that
(1) the same letter of the plain text is invariably represented by
but one and .always the same character of the cryptogram, and
(2) the same character of .the cryptogram invariably represents one
and always the same letter of the plain text, * * ‘ :
in. multiliteral substitution with variants it will be seen that
. . ... - _ - --..if
(1) the same letter of the plain text may be represented by one
or more different characters of the cryptogram, but ■ ■ * "
(2) the same character of the cryptogram nevertheless, .jjjyariably
represents one and always 'tlie same letter’ of the. plain text r ...
^8, Simple types of cipher alphabets with variants . — a. The mat-
rices shown on the next page provide some of the simpler means for
accomplishing monoalphabetic substitution with variants . The systems
incorporating these matrices, are extensions of the basic ideas of multi-
literal substitution treated in par. ' 52. The variant equivalents for
any plaintext letter maybe chosen' at will; .thus, in Fig . 26, Ep=10, 15,
60, or 65; in Fig. ’27, Ep=/sU c , AZ 0 ; FU C , FZ C , LU C , or LZ C ; etc.
p
Cf. the title of the preceding section, "Multiliteral substitution
with single -equivalent cipher alphabets." ..... . ... .
. j 1
t '
• if
. --~r- *
rr; -'T-
RESTRICTED
122
-REF ID: A568 95
RESTRICTED
6 l
7 2
8 3
0 5
6
7
'0
9 0
V W
X
Y
Z
3
2
3
4 5
Q
R
s
T
U
;
'
A
E
I
0
U
A
B
c
D E
L
F
A'
A
B
c
D
il
T
N
H B
A
B
c
D
Kl
F
G
II I-JK
M
G
B
F
G
II I-JK
V
P
J C
F
G
II I-JK I
L
M
N
0 P
N
II
C
L
M
N
0
p
¥
Q K D
L
M
N
0
P
a
R
S
0? ti
0
I
D
Q
R
S
T
u
X
R
L F
Q
R
S
T
U
V
¥
X
Y Z
- P
K
E
V
»T’
W
TT
X
Y
z
Z
. J J-. j l ’
S
M G
* .-**
V
¥
X
x
V
z
“H
Figure 26
Figure 27 1
■ff f —
Figure 28
<«ftl - ' "** 1 #
•- V ¥ X Y Z
. 0
. I"'>' • r ’
Q R S T U
"MH
Z '■
•l h ¥ o‘p ■ ■ ■ ■■
J K' £ ;
' ’ / * _ ‘ _¥ XT Y
: -f g"h i ic !''■ *
F G'S I
'■ 8TUT
AB.CDE
ABODE
NOPQ
V Q L F A
W R H G 13
X S N H C
Y T 0 I D
Z U P K E
ABODE
0 M J F A
E N A L U
M J F A
ENALU
F G II I-JK
•HKGB
T R S F ¥
KGB
a? R S F ¥
L M N 0 P
LHC
OI-JH Y X
LHC
OI-JH Y X
Q R S T U
I D
D C M V K
I D
D C M V K
V ¥ X Y Z
E
P G B Q Z
•— A - _
E
P G B Q Z
Figure 29
Figure 30
Figure 3l
7 4
8 5
96
123^567890
- -Figure' 32'
123456789
ABCDEFGHIJ
7 4 1
ABCDEFGHI
KLMNOPQRST
852
JKLMNOPQR
U V ¥ X Y Z . , : ;
9 6 3
STUV¥XYZ*
Figure 33
5 i
6 2
7 3
8 4
123456789
123456789
ABCDEFGHI
0 8 5 1
TERMINALS
JKLMNOPQR
962
BCDFGHJKO
STUV¥XYZ1
2345 6. 789 0.
' • 7 3
4
PQUV¥XYZ1
2345678 90
.1 - ■* • r -»■■ r • *
• , Figure 34
* » L*"
. - •’ .*A
Figure 35
RESTRICTED
123
REF ID: A5 68 95
b. It is to be noted that encipherment by means of the matrices in
Figures 27, 28, and 31 is commutative j i.e., he coordinates maybe read
in either row-column or column-row order without cryptographic ambiguity,
since there is no duplication between the row and column coordinates.
The remaining matrices above are ' non-c,ommu Native ; therefore a convention
must be agreed upon as to the order of reading, the coordinates It should
also be noted that inFigs^. 30 and 31" the ^letters .in’ th<j. square hqve been
inscribed in such a manner that, coupled "with .the particular arrangement
of the row and column coordinates, the. number of variants available for
each plaintext letter is roughly proportional to the frequencies of the
letters in plain text. A similar idea is fqund in Fig. 35, wherein the
top row of the rectangle contains, a word composed of .high-frequency let-
ters, and the coordinates are arranged in a manner roughly corresponding
to the frequencies of plaintext letters. The matrix in Fig. 28 is a mod-
ification of the pseudo-code system described in par. 52h, with the added
feature of variants. k -■ .t . , ± w-
c. Other simple ideas for producing iFnriant .systems ai?e matrices'
such as the following: * ’ ‘ ' w ‘ ~ : N ^
: . • 1 . 1. .1 . - 1 - 1 * ? /
T. U
V X
A B C 0 E F G II I-J K L II N 0 F Q R S T. U . V yt\ X Y Z.
08 09 10 11 12 13 14 15 Id 17 18 19 20 21 22 23 24 25 01 02 03 04 05 06 07
35 36 37 38 39 4o 4i I12 43 44 l'-5 46 47 48 49 50 26 27 28 29 30 31 32 33 34
68 69 70 71 72 73 74 75 51 52 53 5 1 ' 55 56 57 58 59. 60 61 62 63 64 65 66 67
87 88 89 90 91 92 93 94 95 96 97 98 99 00 76 77 78 79 80 81 82 83 84 85 86
Figure 36
E F
M N 0
Q R
T U V W
l4 15 16 17 18 19 20 21 22 23 24 25 26 01 02 03 04 05 06 07 08 09 10 11 12 13
27 28 29 30 31 32 33 3*1 35 36 37 38 39 40 4i 42 43 44 45 46 hj 48 4-9 50 51 52
58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 53 54 55 56 57
81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 79 80
Figure 37
In these' two matrices there has been a regular inscription 61' the dinomes
in the rows . furthermore, in Fig. 36 the dinomes 01, 26, 51, and 76 (i.e.,
the lowest number in each of the four sequences) give the key word (TRIP)
for that matrix; and. in Fig. 37, the dinomes 01, 27, 53, and 79 denote
the key word (HAVY) for thab matrix. The security of systems involving
such matrices would of course be greatly improved if the dinomes. vere .
assigned in a random manner; but bhon the easy mnemonic feature of the
four sequences and the key word would be lost.
REPTRICTE&
'REF ID: A5 68 95
a. interesting adaptation in a disc form of the typo of matrix
illustrated in Fig. 37 is the following device reputedly once used by
the Mexican Army: ’ -
The device consisted of five concentric discs, the outer disc "bearing the
2 6 letters of the alphabet, and the other four bearing the sequences
01-26, 27-52, 53-78; and 79-00* The rotatable discs made it possible to
change the keys at frequent intervals, without the necessity of writing
out a new matrix each time. -> •' *• • * • • - * J* •
r «is m r i .1 ni * i -*»/ L a l
1 *- - r 1
* * , i. ’ ■ ** ' 1 V l A JU-
39 • More complicated types of cipher alphabets with variants * —
a, Matrices such as those in Figs, 39* and 40 Wlov are termed
frequential matrices , since the number Of cipher values available for any
given plaintext letter closely approximates it’s relative plaintext fre-
quency.
i « flft .TT
* «v‘ ml
. * . -L L i J
“W - 'j, I*
A. 6 0 *D E
• ■ ■ if. > < • i
V W. X Y Z
- . A
T G A .U R
'T E C A P
TL
S'LIEY .
F.RHST
C N D 0 M .
. . E L T I H
• ■ ■ n
RAPT F.’ "
V.Y s.o'v
U. -
- 1 1 , •
N T X N E
CERE?
*" ^ a ■
* 7
•
■a
+ 1 *
1 >1
*vi ‘ ■
V
H 0 A T E
‘A L E’Z’H
V ■
I H R 0 Q
ETRBT
-,r . X,
0IETA-,
. .CNPES
Y
F T L 0 S
AMT I U
Z
I S N D R
IED0N
(676 - cell matrix)
Figure 38
REDTRICTED
125
RESTRICTED
REF ID: A568^5
• I s
6
8
9
1
5
4
3
1
7
2
1
• *
A
1
2
3
4
6
7
8
9
T
A
A
A
C
D
E
E
I
L
N
E
If
T
R
u
C
K
I
If
G
l
A
A
C
D
E
E
II
K
If
0
1
Q
U
A
R
A
If
T
I
E
E
3
A
B
D
E
E
II
J
If
0
R
2
U
If
E
X
P
E
If
D
E
D
8
A
D
E
E
H
I
If
0
R
S
3
I
M
P
0
S
S
I
B
L
E
9
C
E
E
G
I
Iff
0
R
6
T
4
V
I
C
T
0
R
I
0
U
S
2
E
E
F
I
M
0
Q
S
T
T
5
A
D
J
U
D
I
C
A
T
E
i
E
F
I
M
0
P
R
T
T
U
6
L
A
B
0
R
A
T
0
R
Y
5
F
I
L
N
P
R
S
T
U
X
7
E
I
G
H
T
E
E
N
T
II
6
I
L
H
P
R
S
T
U
W
y
8
If
A
T
U
R
A
L
I
Z
E
4
L
If
0
R
S
T
T
V
_y
_z
--9
T
_W
E
If
T
Y
F
I
V
E
Figure 39
•
1
w
• ■ • 1 -i fr -
■ _JL
t- t
1
Figure 40
b. In the fragmentary matrix illustrated in Fig. 38 , "the number of
occurrences of a particular letter within the matrix is proportional to
its frequency in plain text; the letters are inscribed in a random manner,
in order to enhance further _the security of’ the system. In Fig. 39} we
have a modification of the idea set forth in Fig. 38 # except that the
size of the matrix has been reduced from 26 x 26 to 10x10; in this case,
the letters (with appropriate number of repetitions) have been inscribed
in a simple diagonal route (lower left to upper right) within the square,
and the coordinates have been scrambled, for greater security. In Fig.- 40,
there is illustrated a type of cipher square which is known in crypto-
logic literature as the Grandpre cipher ; in this Square there are in-
scribed ten 10-letter words containing all the letters of the alphabet in
their approximate plaintext frequencies. These ten words are further
linked together by a 10-letter word" which appears vertically in the first
column, as a mnemonic feature for the inscription of the words in the
rows. ■■
c. The frequential-type system represented in Fig. 4la (enciphering
matrix) and 4lb (deciphering matrix) was described by Sacco?, who pro-
posed that the dinomes inscribed in -the enciphering matrix be thoroughly
disarranged by applying a double transposition to -the dinomes 00-99 as a
means of suppressing any patent, relationships among the variant values
for the various plaintext letters; furthermore, ’the nulls incorporated in
the matrix were to be used occasionally during the,' encryption of a mes-
sage, in order to throw a cryptanalyst off the track, ’in this example the
number of variant values for ^each plaintext letter has been established,
of course, from the ’standpoint of Italian letter frequencies.
. J* f
^ Sacco 3 Generale Luici, flariuale^dl Critto^rafia, 3d Ed., Rome, 19 ll *7i
22 . ... - - .
126
+ mm I
REF ID : A56895
Nulls
A.
E
I
M
Q
V
one
I18-56
03-25
10-35
10-23
39
SO
02-86
44
21-09
52-62
37-65
53-75
68
77
66
76-54
79-69
71 -78
82-87.
42-12
N
R
mi
two
64-74
55-14
83-90
63-06,
47-45
.28
38
70
97
P
II
08 ■-
17
80
43
13-73
T
33-88
seven
46
eight
29
Y
four
22
27
Z
five
34
60-91
59
six
Ok
period
l6-6l
( 1
J“ . ^ 4*-
Figure 4la.
_ - ,
,fwr*V * "* 1
• 1 . . 2 3
_ V». r t .{«r > . L * J . -
3'*"V- 5 , 6
F
S
0
M
Q
E
I
T
G
P
0
D
-.9 '
<t
zero
I
eight
Q
M
0
f
mm
B
z
three
A
five
A
C
0
D
U
-
-
U
Figure 4lb,
127
REF ID: A5 68 95
RESTRICTED
I f s V*
, d. The Baconian cipher described^ in par. |53a may “be used as' a basis'
for superimposing additional complexities . _ For instance^ the' "a" elemehts
may he represented hy any one of the 20 consonants as variants^ while _ ’ t
the "b" elements may he .represented hy any one of the six vowels; or the f
letters ‘A-M may he used to represent the “a" elements and the letters'
N-Z forthe "h" elements; digits may he used for the "a" ; and "h" elemgpts,
.either bn the basis of the” first five and last five digits, or on the* "
basis of the odd and even digits; or the first l6 consonants (B-M) and
the last 10 consonants (N-z) may he used for the "a" and ( "b" elements
. with the vowelB used occasionally as nulls — thus thc.restQ.tant crypto^,,^ *
grams will resemble those of a fairly complex cryptosystem. ‘Howler,*"
once the cryptanalyst assumes the possibility of ( such" a system, its com-
plexity is more apparent than real._ Similarly, variations of this genre'
may he superimposed on triliteral systems such as the Trithemian 'cipher 1
illustrated in par. 53b 5 variants for the "1", "2", and ,T 3” elements may’
he chosen in such a way as to provide a large number of equivalents " for
ie$.ch basic triliteral jeomhinatibn.
e. Another scheme, for a complex variant system is a summing -tr inome
systemT In this cryptosystem, each plaintext letter is assigned a unique
value of 1 to 26; this value is then expressed as a' trinome", the digits
of which sum to the designated value of the JLetter . "For example, if a
letter has been assigned the' value "4", it may be represented by any one
of the following permutations apd’ combinations 11- : . , . _ v , : -
ooh
031
vll2
'202
- t * * T » * ^
301 * ,
013
o4o
121
■ 211
310. . , _ .
022
103
130
. 220
400 ; . ,
M ‘ * -
• * M
Since the values toward the middle of the range 1-26 may be represented
by a very considerable number of surraaing-trinoraes (e.g., for tfie values
13 and l4 there are 75 variants each), such a system would offer a crypto-
grapher wide latitude in the choice _of cipher equivalents in enciphering,
'! — / _ - • r - ... . . T
A.
^ The representations of an integer (i.e., a whole number) as the sum
of integers in all possible ways are termed the partitions of that num-
ber. The partitions in this subparagraph are mod 10 and also include the
digit 0 in order to form trinome equivalents out of all the possible per-
mutations .
reotrioTed
128
REF ID: A56895
RESTRICTED
especially if the "basic values of the plaintext letters were chosen to
correspond with the scale of their relative frequencies, such as the fol-
lowing : . ' '
J <4 B W Y U F H D I ON S"'T' R A S L Of U'Z "
01 2 3456789 10 11 12 13 14 15 16 17 18 19 20 21 33 23 34 25 186 37
.. ******** SPSS*”
‘ m&'ggumgw m
* - - ■ m u % n u m
• •
• • ^ M a* * 0 * ^ * * s * * % &
•K -*
l T- *
; yr.r
~4. ^
(rj
■ < <*- -v
^ or
..r sri * g * s? ^ ^ * “
? g .£ * *• **
- -:^ ■% * * w c ^ * m
■ - m * % g m ?' i ^
f > * 3*P1fe . S’ gfgggs
r ^■■V 5Vi k-r^^s^
* ‘J 1 . :V £ ±>'£ * WM%
-* •* rtv - v* » >-*»> ■ - t; a - -’ 4
i.T-
, *S ■
r»r.
" ' /"VvV •* ' ._> ~%£5 JfMf'n a _*»£ «.? a 5- — » „
The tallies beneath each valtfe' represent the number of variants possible
for the particular value . The unused values for 0 and 27 (uniquely re-
presented by 000 and 999, respectively) may be used for punctuation marks,
nulls, or other special-purpose symbols. Since such a system, once sus-
pected, would offer little difficult y^ to a cryptanalyst, certain modifi-
cations would be necessary in order to pose any real obstacles in the way
of solution. For instance, if the numerical value [of a letter is expres-
sed by permutations of 3 letters ’(instead of digits') out of a set of the
10 letters A-J wherein’ the sequence of the letters A-J represents a dis -
arranged sequence of the digits 0-9, such a system may be among the most
complex types of ciphers in the realm of, mono,aJphabetic substitution,
requiring the solution of many simultaneous equations, A further refine-
ment would involve the use of all 2 6 letters as variants, in predetermined
groups, to represent the digits ^-9. Fortunately for the cryptanalyst,
such systems are impracticable for field military usej but if they were
encountered, a sufficiently large volume of text, coupled with Hitt’s
four essentials quoted in Section I, would eventually make a solution
possible. The/ actual crypt analytic complexity of certain apparently
exceedingly complex cryptosystems is dependent on their being correctly
used at all times, which is not invariably the case with military ciphers.
, ^ 7" '
•' J The sblution would involve simply dividing the cipher text into
groups of 3 digits , summing the trinomes thus produced to yield 28 pos -
sible basic values, and solving these basic values as in any simple mono-
alphabetic substitution cipher.
, REBTRICTEB
129
-RESTRICTED
REF ID: A5 68 95
60. Analysis of simple examples . — a. The following cryptogram is
available for study:
Q
M
D
C
V
P
L
F
R
F
D
H
R
W
J
W
L
K
D
K
R
H
B
P
V
R
L
T
V
M
B
K
L
W
D
W
V
H
V
K
S.
H
B
C
L
P
-Q
K
J
R
V
vr
S
M
L
K
G
C
R
R
L
R
R
K
V
M
G
F
X
W
J
R
G
M
V
VI
G
T
J
H
Q
K
X
F
R
Z
V
F
D
M
L
T
B
P
L
P
V
F
L
M
D
C
N
W
N
H
B
C
V
Z
R
L
VI
Q
F
D
H
D
W
V
Z
B
R
V
K
L
C
V
C
V
R
D
H
L
R
V
T
L
F"
R
C
D
K
G
M
X
VI
X
M
D
T
S
C
B
C
L
Z
L
R
L
M
V
T
9
Z
N
K
9
VI
V
P
B
R
R
C
L
R
X
R
D
C
N
K
V
P
B
T
R
T
G
H
J
Z
L
F
Q
F
V
K
B
w
D
Z
X
P
R
H
S
P
G
H
L
K
L
F
V
Z
L
T
V
M
L
K
D
P
Q
R
i/
Z'
L
z
D
T
B
M
R
T
G
M
N
Z
V
F
X
K
9
F
D
C
L
Z
V
T
V
F
D
F
V
R
G
c
L
P
Q
P
R
C
D
W
V
R
J
T
R
H
L
Z
L
M
V
W
R
P
V
P
D
Z
D
VI
J
p
R
W
L
R
J
X
V
M
X
M
D
T
9
M
G
F
D
R
D
K
L
W
J
F
L
P
J
¥
' §
F
Q
VI
B
F
R
c
B
Z
D
K
V
VI
G
Z
S
H
B
H
D
H
J
C
X
The first thing that strikes the eye is the total absence of vowels , re-
markable not only because six letters are missing (cf. the A test) in a
text of this size, but also' because all six of these letters fall into
an identical limited category — a significant non-random phenomenon. Since
a uniliteral substitution alphabet with six. letters missing is highly
improbable, the conclusion of multiliteral substitution is obvious.
Upon closer inspection it is found that, if the cipher text is divided
into pairs of letters, only ten consonants (BDGJLRQSVX) are used
as prefixes, and the remaining ten consonants (CFHKMPRTWZ) are
used as suffixes --thus the biliteral (and bipartite ) characteristics of
the cipher text are disclosed. A dlgraphi'c? distribution is therefore
constructed: - •
c
F
H
K
M
p
R
T
W
z
B
^ 1
s=r
cs
- ‘ D
5
g
_
_
=x
S
rr
G'
r=
ss
S3
5
J
_
|B|
_
sa
_
L
.
77
gr
5=
ssi
, R
==■
s
H
, .
j ^
S3
H5
' Q
■a
sr
_
.
, . s-
-
S3
rs
—
__
r
_
§
a
=
=
•55
X
ss
1
\ If it had not been noticed that the cryptogram should be divided
into > pairs for analysis, a biliteral distribution (see par. 23d) might
have vjpeen made, in order to reveal contact affinities of the cipher let-
ters .
RESTRICTED
130
ItEOTIlICTEP
REF ID.: A5.S8 95
L •
- , ■ ^ , r , -*■ - . J- - ” i — * '*
' r . ,b. It is possible that the cryptogram under study may involve the
use of a small enciphering matrix with variants for the rows and cblumns .
Sine?, there is available an easily-applied special solution which permits
the determination of the row indicators which are equivalent (i.e., inter-
changeable variants) and the column indicators which are equivalent, mere-
ly from a study of the digraphic distribution, this possibility is examin-
ed. The special solution is based on the following considerations: in a
■ message of moderate length for such a cryptosystem, it may be assumed
that the various possible/ cipher pairs for a /given plaintext letter will
' be used with approximately equal frequency; for this reason, the cipher
letters which pair with one of the letters used to indicate . any particular
- row jDf ,thq„, enciphering matrix may be expected to pair equally often with
any other cipher letter which has been used .to indicate the, same, row, (and,
of course, the same is _true. concerning the,, column - indicator letterr). .
Thus, in the digraphic distribution, of such. a cryptogram, .sets .of rovus
appear which have similar "profiles" and, likewise, sets of similar col-
umns. 7. First, a study will be .made of th^ ^oys^of the. distribution just
compiled^ in an attempt to. .locate, and, isolate tiioge 3 /hich match . with each
‘ "other;" then, 'the same will be done with the columns of the distribution.
c. It is noted that the "L" and. "V" distributions have pronounced
similarities (Fig. 42a) — these rows came 4, under consideration first because
of their unique "heaviness" of their frequency characteristics. Likewise,
the "D" and "N" rows have homologous attributes in their appearance (Fig.
42b) , However, the further grouping of the rows by ocular inspection may
. present difficulties to the student, since b-s may not yet trust his eye
»— ■
%
3.
—
s
—
s
=
31
3
ir=
Figure 42a.
• *■ 1 " ' * — ■
<« ^ l ' I'-'
i* i ;
D
N
- Figure 42b .
in matching distributions; and he may feel the need for some kind of
statistical assurance. In the following subparagraphs there is given the
technique of a more precise method for matching, mathematical in nature.
. . , #1 . 4 . 4 - 4 - I * * ’4 '« r
7 — - * -
1 These similarities are especially pronounced when the encipherer
uses a "check-off" procedure for choosing his variants for each letter,
that is, when he systematically "checks off" the variants used during
encryption to instire that all possible variants are used in approximately
equal proportions .
REOTRICTEP
■ 131
REF ID: A5 68 95
RESTRICTED ,
d. This method of. matching in an attempt to ’’equate" interchangeable
variants involves computing a separate value for each trial matching of 'a
particular row (or column) against each of a series of other rows (or
columns, as appropriate) — such a value is taken as an indication of the
"goodness of match" exhibited. by the particular trial, the theory being
that the correct match- wj.ll produce the highest value.® -The value for a
particular trial match is computed by multiplying the number of tallies
in each cell of ope row :(or column) by the number of tallies in each cor-
responding cell,, in the other. t row (or column) and then totaling the pro-
ducts thus obtained,/, Because. ,6^ the way in which it is produced, such a
value is termed a "cross -products, sum" . . , .mi— -
"e'.' "In’ subparagraph 6 above’, it’ was determiriad that the "L” and "V"
rows wefe equivalent,’ and that ’theV'D" and "W" rows also formed an equiv-
alent pair. The next* "heavy" row is the "G" rowj' r tfii.6 is xo be tested"
for match with the five remaining 'unmatched rows !,' Let the *"G" row be
tested first ’against the* "B" row. tnese two rows are given below, with
their cross-products Sum. ’ For convenience, the cross-products sum is
symbolized by ?^(© 1 ,0 2 ), where ' ©1 and 02 represent jfche designators of the
distributions to be matched. 9 * '
.jf r» — I < "« •- t » i . « * ^
i\ . "G'V 2 2 2 - u -3 - - 1 - 1
- ■■ *-"B" : 3111122121.
^ (G,B) : 622-3--1-i = 15 r
P T / vJ. , , * . . ^ _ ‘ * r * XS 1 • • • • X * • - *** S \ i '
The complete table^pf the comparisons of the.. "G" ..row with .the five .avail-
able rows is as follows :
6 2 2 - 3 - - 1 - 1 ? 15
2 2 2 - 3 - - 1 - 1 : 11
_ 4 - - 3 - - - r r - = 7
2 4 4 - 6 1 = 17
- 2 - - 6 '-=8
The results indicate that the most probable match with the "G" row is the
"S" row.
X (G,B) :
xM*
j|r(G,Q) :
% G,S :
^(G,X):
f . Since, the next "heaviest" row to be tested is the "B" row, its •
matchings with the .three remaining rows are made, and are given below:
^(B,J): 311112412 l r 17
X (B,Q): -2-2122 - 2*1 - 12
X (B,X): -1-1222-4-= 12
* , Nr f » "f fc - r * : ~ /ft » ••
(J •
0 In this connection, note
. , vi • j
° The Greek letter ^ (chi)
matching operations.
the considerations treated in^ubpsr . 60 ^.
is often \tsed in cryptology to symbolize
l
» ii
■ I r.* - 1 j ■ - j , * - r *4 -' '
■* H.r u 1 . Tf r - f '»* I .
RESTRICTE D
132
REF ID : A56895
RESTRICTED
The correct matching, of the "B" and " J" rows is indicated by the results »
This leaves only Hie "Q" and "X" rows , which are presumed to go together,
since not only is their cross-products sum satisfactory (when compared to
the % values Tor some of the other rows which have "been matched), "but,
equally important, their patterns of crests and troughs are similar*
Since we have not found more than two rows for any one set of inter-
changeable values, ifc appears that the original matrix hadonly five
rows, with two variants for each row. The rows, of the distribution dia-
gram are therefore combined in the following diagram:
CFHKMPRTWZ
BJ
DN
GS
LV
.QX
4 22223 4 232
82872225 7 5
344 - 51 - 1-2
2817789677
-3-3322-3-
Figure 43
g. Analysis of the distributions of the columns of Fig. 43 quickly
reveals that columns "C" and "H" may be matched as a pair, and likewise
columns "F" and "M”, and columns "P" and ,T R" . In order to decide the
groupings of the remaining columns, the six possible V values are der-
ived:
*(K,T):
4
35
- 42 - =
81
Combinations :
4
49
- 49 9 =
113
KT,
WZ:
81 + 90 =
171
i(K,Z):
4
35
- 49 - =
88
KIT,
TZ:
113 + 73 =
186
J(T,W):
6
$5
’-"42 - =
83
kz;
T If:
88 + 83 =
171
£(T,Z):
4
25
2 42 - =
73
jc(W,Z):
6
35
- 49 - s
90
» \
_
, .
_ r .
I h. The groupings of the columns having been determined, the fre-
quency diagram is reduced to its basic 5x5 square, and the $ test is
II
C • F K P T
H M W R Z
BJ
6 4 5 7 4
DN
16 4 14 4 3.0
GS
7 9-13
LV
3 15 l4 17 13
qx
- 6 6 4 -
4 p =1962
$r=H32
4 . 0=1670
taken as further statistical '.assurance of the matchings. Although 4> 0 in
this case does not come up to the best expectations, we feel nevertheless
that the matching has been carefully and correctly accomplished, and so
K-'l
RESTRICTED
133
REF ID: A5 68 95
ItEQTRICTED
the next step is continued with a conversion of the multiliteral text
into uniliteral equivalents, using the following reduction square con-
taining on arbitrary sequence:
C
F
K
P
T
II
M
W
H
Z
BJ
A
b'
C
D
E
BN
F
G
H
I
K
GS'
L
M
K
0
P
LV
Q
R
S
T
U
V
W
X
Y
Z
The converted cryptogram is now easily solved^ using the principles set
forth in Section VI. The first fifteen letters of the plaintext message
are found to read ‘LEATHER FORECAST ", and the original enciphering
matrix is recovered, based on the key word ATMOSPHERIC, as follows:
p
F
C
K
T
R
M
H
W
Z
• J LV
A
T
M
0
S
-f-i J n
P
II
E
R
I
« BJ
C
B
D
F
G
GS’
K
L
K
Q
U
ox
V
W
X
Y
Z
* ■ — •
i. The method of matching rows and columns just described in the
preceding subparagraphs applies equally well to all the matrices in Figs .
26-35, and similar variations. If in the process or equating indicators
the cryptanalyst" sees that the row Indicators ore falling into the same
groupings as the column indicators, he might be able to accelerate the
equating process by taking advantage of this feature alone, as would be
the case if he had encountered a cryptogram involving a matrix with .indi-
cators arranged in a manner similar to that shown in Figs. 29 and 30.
Furthermore, a cryptogram enciphered in a commutative system, wherein
the equivalents have been taken in row-column and column-row order indis-
criminately, may be recognized as such through a study of the digraphic
distribution of the cryptogram since the " <* " row of the distribution /
will have an ajjpearance similar to the " «* " column, the " P " row will j
be similar to the " P " column, etc; 10 this matter is discussed further in
subpar. 6ld. 1 •
10 It is often convenient to use arbitrary symbols in cryptanalytic
work, to prevent confusion with designations of actual elements of plain
text, cipher text, or key (see footnote 1 on page 58) . For this purpose
Greek letters ore often used^ for reference, the 2 H letters of the Greek
alphabet and their names are 'appended in the chart belov: . (
A alpha
E g epsilon
I u iota
hi *r nu
P p ro
<p f Phi
13 p beta
Z C zeta
K i< kappa
31 t xi
€. c r sigma
X ^ chi
r gamma
H eta
A ^ lambda
O «. omicron
T -c tau
V f psi
A £ delta
0 $ theta
A\ f *. mu
H -rr Pi
T v ypcilon
jTL co omega
- REE -ID: A5 68 95
, RESTRICTED
t
.c
It to important to point out that in matching, the ci-yptanalyst
should begin with the "host’' rows or columns — hoot not. only from the
standpoint of "heaviness”, of the distribution, but also best from the
point of view of a distinctive pattern of crests and troughs. If insuf-
ficient text is available to allow equating all the interchangeable
coordinates of a particular enciphering matrix, it may still be possible
that a conversion of the cipher text by moans of a partially-reduced re-
construction matrix may yield enough idiomorphic patterns and other data
to make possible an entry into the text. If the .cryptographer has not
used a "check-off" process in enciphering, but instead has favored certain
equivalents for the various plaintext letters, matching may not be pos-
sible; nevertheless, an entry into the text may be facilitated in this
case, because some of the resultant peaks in the cipher text may be cor-
rectly identified. Furthermore, since no variant system can possibly
disguise the letters of low frequency in plain text, their low-frequency
equivalents in the cipher text may provide possible approaches to solu-
tion. (See also subpar. 6 le) .
k. In addition to the method of solution by matching and combining
rows and columns of a digraphic distribution of a multiliteral cipher,
there is also the general approach applicable without exception to any
variant system. This method, involving the correlation of cipher elements
suspected to be the equivalents of specific but unknown plaintext letters,
is treated in detail in paragraphs 6 l r and 62.
l . Systems such as the Jl— level dinome cipher illustrated in Fig. 36
are susceptible to a very easy solution, if the dinomes have been in-
scribed in numerical order ?>*• ,v »dicated. .Assuming such a case in a
specific cryptogram, thfe first six groups vC which are
68321 09022 u 4 8057 65111 88648 42036 ..
a four-part frequency distribution, of, the. entire message, is taken as
illustrated in Fig. 44 - below: - * - ^
_ - - - t i _4 * i,"*' < * ’
‘ . - ' _
01 02 03 64 ol 8 07 08 09 5 il 13 14 15 .16 17 S 19 20 21 £ 23 24 25
. . - - t . ' ••• -j*
• w +
m fc - -
= _ ~ __ ’=? l_' ^ ijr 5 ' == ^ ^
26 27 28 29 30 $i- 32-^33 34 ^5 36 37 38 39‘4o 4 i 42 43 44 45 46 4-7 48 49 50
k »r , 14 « * * ■* ’ ■* • m \* 1 , *
-- r- 1 * -
“ ** t t- ~
• > . ■ • • * 1 *i '
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 1 68 69 70 71 72 73 74 75
76 77 78 79 80 81 82 83 84 8 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00
Figure 44 .
1
REOTRICTEB -
135
REF Id : A56895
RE S TRICTED
j If the student will bring to bear upon this problem the principles he
learned in Section V of this text, he will soon realize that what he' now
/ has before him are four simple, monoalphabetic frequency distributions
similar to those involved in a monoalphabetic substitution cipher using
standard alphabets . The realization of this fact/ immediately provides
the clue to the next step: " fitting each of the/distributions to the , „
normal”. (See par. 31 ) • This can be done without difficulty in this
case (remembering that a 25-letter alphabet is /involved and assuming that
I and J are combined) -and the following alphabets result:
-01— I-J
26— U-
51— N
76— E
02— K
27— V
52—0
77— F
: 03— L
■28— W
53— P
78— G
■ 04— M
29— X
54— Q
79— H
05— N
30— Y
55— R
80— I-J
06—0
31— Z ‘
56— S
81— K
07— P
32— A
57— T
82— L
08— Q
33— B
58— U
83— M
09— R
34— C
59— V
84 1 -r-N
: 10— S
' 35— D
60— W
85—0
' 11— T
36— E
61— X
86— P
12— U
37— F
62— Y
87— Q
13— V
38 — G
63— Z
88— R
14— W
39— H'
64 —k
89— S
. 15— X
40— I-J
65— B
90— T
16— Y
41— K
66— C
•91— U
17— Z
42— L
67— D
92— V
18 — A
43 — M
68— E
93— W
19— B
44— N
69— F
94— X
20— C
4.5—0
70— G
95— Y
21— D
46— P
71— H
96— Z
22— E
. 47— Q'
72— 1-J
97— A
23— F
48— R
73— K
98— B .
24— G
49— S
74— L
99— C
25— H
60— T
75— M
00— D
The key word is seen to be JUNE and the beginning of the cryptogram is
deciphered as "EASTERN ENTRANCE "
m. If instead of 25-element alphabets, a system* such as that in
Fig • 37 has been used, only a slight modification yf the procedure in
subparagraph would have been necessary, i.e., ^he' distributions would
have had to be considered on a basis of 2 6, and the process of fitting
the distributions to the normal would have gone on as in the previous
example * .
RESTRICTED
-136
REF ID: A56895
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nr.u - E" a 1 :
n. . One further application of principled learned in Section V, .de-
served to "be mentioned here, in connection With the solution of systems
such as those of Pig. 36 . Let the following short message "be considered:
lV -ii . -*• r { ' ‘ • * - * «Tl±i£P.i,
4 8 g'YS' 8842 3 52099 9360 4 7 6 059 05651
36683 "52 267 97 11 4 5446 r 6 76
kl .. , 1 *’^ >r *1 r> 7 TT.rT. V* h ~ ^ v, •* ^ * ;
If ib is ,known bhat’the' correspondents have been using a variant system
such as- that in Pig. 36 ,. a special solution. may he employed, in those cases
wherein there is insufficient cipher texb to permit ( analysis by the method
of fitting the frequency distribution to the normal]. Thus, a' short cryp-
togram may he solved hy a variation of ^he plain-component completion
method described In par. r 34.H First, let the cryptogram be copied in
dinomes', With an indication o’f the level (l.e., the; "alphabet" ) the di-
nome Would ’occupy in thfe 4-level matrix; thus:
, ; . . k ■ ■.,* .. J /-*■* r J • -• *' :
48 22 68 84 23 52 09 99 36 04' 76 05 go 56 ~51 36 68 35 22 67 97 11 45 44 66 76
2 1
T T
141433232
“T ■*' . , . ”
1 3 4 1 2 2 3
. 1 i » *% %
« i n -- * ■
1 - ij .« *
I., * 4 15
,U. 1 j •• #/ ^
2 1 34 1 3 1
< • Si ;
The dinomes' belonging to the four levels are as follows:
x. - £* * v ; 2- - ■ .’V * L t . * '-*»'* [ 1 1 *
- r.(l) 22 23 09 04 05 22” 11 * ** ” ’ ’
1 (2) 48 36 36 35' 45 44
(3) 68 52 56 51 68 67 66
.. . (it) 84 99 7 6 90 97 76 ' . .
.... - * ■ . . A ' li. i * * - // ■'<-
, . , _ - - » A JW " . .
These dinoines are' converted into terms of jbhe plain component by setting
each of the cipher sequences against the plain component qt an arbitrary
point, of coincidence, such ''as in the following example :
; a. ; ‘1 -* I 1 /*- '* ‘
A B C D E F G H 3?- J K L M _ W 0 P Q. RSTUVWXYZ
01 ’ 02 • 03 • 04 05 06 07 08 09' io 11 12' 13 14 15 16. 17 18 19 20 '21 '22 23 24 25
26 27 28 29 30 31 32 33 34 35 36 -37 38 39 4o 4l 42 43 44 45 46 ¥7 *18 49 50
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75
76 77 78 79 80 81 82 83 81; 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00
* #
( 2 )
(3)
(4)
*) > -
-22 iff;'
23=X;
09=1;
04=D;
05=E;
224,1;
' : 11=L '
■ " ^
48 =X;
36=L;
36=L;
35=K;
45=U;
41|=T
6 8=S;
52=B;
56=F;
5l=A;
68:S;
6 7=R;
66-q
' V
-2W»:
. 99=Y;
76=A;
90 =P;
97=W;
T6zA •
■
*
•! J
CT.iLT?
t . -
r jr :V
\ »>* 1
• :or.
’ It should be clear to the student that the reason this method epu be
applied in this instance ' is that both the plain component (ABC Z) and
the cipher component ( 01 , 02 , 03 25 ; 26 - 50 , 51 - 75 i 76 - 00 ) are known
sequences (or thus assumed) .
I
1
ttEOTRICTED
137
REF ID: A5 68 95
d vx
RESTRICTED
. o* , .Thf; plain component sequence is now completed on the letters of
the four levels, as follows: • . . . •- .* ' ‘ - ■ ■ ■ >
1 st level
W X I D E W L ‘
X Y K E F X M
Y Z L F G Y N,
Z'AM,QHZp '
A B N H I A P.y ‘
B C 0 I K B Q*
cpp x i.c ■
D E QL'M'DS V,
E F R M.lf E T ’ ’
F G S N 6 F U ”
GHTOPGV
H I U P Q H W
1 X, V Q R IX
KLWRSKY
LMXSTLZ
MNYTOM A’"
NOZUVBB
OPAVWOC
PQBVXPD
QRCXYQB
RSDYZRF
S T E Z A S G
TOFABTR
uif GBC U I., !
V W H C D V K
2 d level
XLLKUT
YKMLVU,
.ZHHHfL
. a °-q ■
BPPOYX;,,
?c Q Q P. 2,.J. ...
MS a Z . .
E p S R B A.
FT T S.C B .
‘G^UTDC
HVVUED
IPV.F.E
K X X W G F
L Y Y X Pi G
M Z.Z Tf.J H. .
N A A Z IC I
0 B B A L K
PCCBHL
QDDCNM
R E E D 0 E
S F F E P 0
T.P GFQP,
u h,h g.r q
V I I,I}S R
W K K ITS
... - 4 . » ■
3 d level
* s - * .*
SBFASRQ
TCGBTSR
UDiqUTS
„ .y, E idvut
.. W ..F K. E W V B .
X Ct L F .X W V
,,.Y.H M,G YXK.
Z jE ,H B Z Y X .
. A K.0LJ.AJB Y
P L P KB A Z
CMQLCB A
, DJ.RHPCB.
EOSHED'Q
F P T 0 F E D
G QUP^G F.E .
II R V Q H G F
I S' W R I H G_
K T X S K I H
LUYTLKI
M V Z U M L K
H W A V N M L
0 X B W 0 N M
p’y C X P 0 a...
q z p x ft p .0
R A E Z R 'QP
i * « , 1 r «. ■ 'i ' ■
4th level
• t* . ‘ T
I Y A P W A
K Z B Q X B
L A C R Y C
HBDSZD
N G E T A E
■ 0 D F U B F
. P E G V C G
QFHWBH
•RGIXEI
SHKYFK
T I L Z G L
U K M A S M
V L H.B IH
IT M 0 C X 0
YBPDLP
Y 0 Q E M Q
.ZPRFMR
AQSGOS
BRTHPT
C S U I Q U
DTVKRV
E U W L S W
. F.VXMTX
GWYBUY.
H X Z 0 V Z
I , It is seen ^hat the , generatrices with the "best assortment-^ of high-
frequency letters for the four levels are: . ,
1 st level .. 2 d level 3 d level l ■ -./ 4 th level
EFRMHET -REdEDOH. E.OSNEDC. 8 C E T A E
* . . - r ,
, r - . r . . ' - . • bi w ■?. • ^
In evaluating generatrices, the sum of the arithmetical frequencies
of the letters in each row may he used as an indication of their relative
"goodness". A statistically much more accurate method of evaluating
generatrices involves the use of logarithms of the probabilities of the
plaintext letters forming the generatrices . (See also footnote 7 on *
page 89 ..) . -- *
RESTRICTED * 138 ‘
■'REF ID: A5 68 95" ‘
i r. | i
If the lcttci'6 of these generatr
ancc of their, (Jinpme equivalents
various levels.
!=■■£»* r v ■ 1 r « '« * , J - j
% generatrices arc arranged in the order pf appear-
juivalents, according to the way they* ’fall" into the
48 22 68 Oh 23 52 09 99 36 04 76 05 90 5 6 51 36 68 35 22 67 97 ll 45 44 66 7 6
E I? . _ R . M N , E T
R E E D .'OR
E. 0 ...... . S N . E D . C
N C E T . , *A E
the plain text "REEKFORCEIvIEpiTjS HEEDED AT ONCE" is clearly seen. Or, more
simply, IT we examine the equivalents of 01, 26, 51, and 76 after the
generatrix determination has teen made, the key word JURE is revea,led.
If an error, had been made in the /selection of a generatrix, the error
could he resolved hy hypothesizing the probable key word, or by decipher-
ing the text' on the basis of the as siuned diagram and then noting and
“degarbling’ tlie systematic errors (which, it would be noticed, all come
from one level) . - *- * 1 •*
1- - «-»*"• *• i.. 1 .' r ; _ ■ . ■ . . . .! • j'i ; ,n-
■ 2* The student should note that no one generatrix will yield plain
text all the way across as in the example in par. 34. Instead, the
generatrices must be considered separately for the four levels, since it
‘Is. within each of the four level’s "that there is a homogeneous relation-
ship of dinomes. Obviously if dinomes from mofe than one level were used
to complete* the plain component sequence,' the generatrices would not con-
sist’ of a - homogeneous 'group of letters but*i"ns'tead would represent an.
assortment of" letters ’ from tiro : or more "alphabets" .
61. Analysis of more complicated examples , — -a. As soon as a begin-
ner in cryptography realizes the consequences of the fact that letters
are used ‘with greatly' varying ‘frequencies, in normal plain 'text, aTbril-
liant idea very speedily comes^to him/ Y7hy not disguise 'the natural fre-
quencies of letters lay a system of substitution using many'equivalents ,
and let the numbers of equivalents assigned to the various letters be
more or less in direct proportion to the. normal frequencies jbf the let-
ters? Let E, for example, have 13 equivalents; T, 9) N, 8; etc., and
thus (he thinks) the enemy cryptanalyst can have nothing in the way of
telltale or characteristic frequencies .to use as an entering wedge.
b. If the text available | for ' study is “small in amount and if the
variant values are wholly independent of' one another, the. problem can
become exceedingly difficult. But in practical military communications
such methods are rarely encountered, because the volume of text is usually
great enough to permit of the establishment of equivalent values . To
illustrate what is meant, suppose a number of cryptograms produced by
the monoalphabetic -variant method described above show the following
139
REF ID : A568 9$
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1 *' *
two sets of groupings.!^ of cipher elements in the text. Set "A" "be la#
assumed to he different representations of one particular underlying
plain text, and Sot "B" assumed to he representations of another under-
lying plain text:
Set "A" Set "B"
( 12-37-02-79-68 -13 -03-37-77 )
(82-69-02-79-13-68-23-37-35)
(82-69-51-16-13-13-78- 05-35)
(91 -05-02-01-68 -42-78-37-77)
(71-12-02-51-23-05-77)
(11-82-51-02-03-05-35)
(11-91-02-02-23-37-35)
( 97 -12-51-02-78-69-77 )
to the following tentative
'its : .
An examination of these groupings would lead
conclusions with regard to prohahle equivale
(12, 82, 91) (02, 51) (13, 42>, 68) (35, 77)
(05, 37, 69) (01, 16, 79) , (03, ,23, 78) (11, 71, 97)
The eotahlishment of these equivalencies, would sooner . or later lead tp
the finding of additional sets of. equal values. The completeness vith ,
which this can he accomplished will determine the ease or difficulty of
solution. Of course, if many equivalencies can he established the prob-
lem can then he reduced practically to monoalphabetic terms and a speedy
solution can he attained. — '
c. Theoretically, the determination of equivalencies may seem to he
quite an easy matter, hut practically it may he very difficult, because
the cryptanalyst can never be certain -that a combination showing what
may appear to he. a variant value is really such and cLop§. not. represent
a part of a different plaintext sequence. ..For. example, take the groups —
17 -82-31-82-14-63, and
: : 27-82 Jl0-82-l4-63
Here one might suspect ,that 17 and 27 represent the same letter, 31 and
40 another letter . But it happens that onq group represents the word
MANAGE, the other DAMAGE. There are hundreds of such c.ases in English
and in other languages . , _
d. When fdverSibie combinations are used as variants, the problem
is perhaps a hit more simple. For example, using the accompanying Fig. 45
* tmi r * ■
■ .. W,S Jt H A__0 E_
F,X _D T M F P_
. . ■ G, J _0 B U I V_
• ,r C,N _G X R C S_
E,T b I L Y 1 W K
" > * f
Figure 45
13 T}i je alert student night he able to determine the underlying p] ain
text of the two sets c'.’ ciphertext gi’oupingc.
K,Z Q,V B)H M,R D,‘L
H
H
A
0
E
D
T
H
F
P
0
B
U
1
V
G
■«r
A
R
c
S
b
L
Y
V
E
l ’:0
RESTRICTED
REF ID: A5 68 95
^ ItEOTRICTED ■-
for' enqiphcrmpnb, two messages with the same initial words, REl'llRENCE ■
YOUR, may he f pnoiphored^as fqllows,: . . . „ v ■■ . . .>
_R E " F E R E ‘ N r C EY OU R
(1) N II W 13 H X L S II C D W W Z N R S L II P S R B J 0 H
(2) CHDWRXSLHN D W Z W N R L S II P R W J BN H
f ’ - ■ * - ■
The experienced cryptanalyst, noting the appearance of the very first few
cipher groups, assumes that not only have the messages identical beginn-
ings in their plain texts, hut also that he is here confronted with a
variant system involving biliteral reversible equivalents. One of the
manifestations of such a cryptos'ystem ‘is that in the digraphic distribu-
tion of the cipher text the "B" row will have an appearance similar to
the "B" column, the "C rt row iri.ll resemble the "C" column, etc . ; thus ,
the cryptanalyst will almost immediately realize that he has encountered
a commutative system involving a matrix smaller than that indicated by
the size of matrix necessary for' making the digraphic distribution.
e. The probable-word method of solution may be used, but with a
slight variation introduced because of the fact that,' regardless of the
system, letters of low frequency in plain text remain infrequent in the
cryptogram . Hence, suppose a word containing low-frequency letters, but
in itself a rather common word strikingly idiomorphic in character is
sought as .a "probable word"; for example, words such as CAVALRY, ATT ACK,
and PREPARE, Such a word may be written on a slip of paper and slid one
interval at a time under the text, which has been marked so that the
high- and low-frequency characters are indicated. Each coincidence of a
low-frequency letter of the text with a low-?raquency letter of the •« -
assumed word is examined carefully to see whether the adjacent text let-
ters correspond in frequency with the other letters of the assumed word;
or, if the latter presents repetitions, whether there are correspondences
between repetitions in the cipher text and those in the "word. Many trials
are necessary but this method will produce results when the difficulties
are otherwise too much ^ for ^the_ cryptanalyst .to overcome; >■-
->■» r i i-> i J,il — .• -v-iV ..4. ^ * - i •i r ; >'7 X „!V_ — “ ‘ * ' ’ "~ c ~ '
62. Analysis involving the \ise , of j sglogs — a. In military communi-
cations it is not unusual that cryptograms are prpduced containing identi-
cal plain text but which have been subjectedto different cryptographic
treatment, thus yielding different cipher texts. This difference in cryp-
tographic treatment may be caused by the use of .an entirely different
general system, or by the use of a different" specific key, or merely by
the choice of equivalents in a variant system. "Messages which present
different encrypted texts but" which contain identical plain text "are
called isologs (from the Greek iso ’= "equal" ‘and logos = "word"). One of
the easily-noted indications of the ^possible presence of isologs is
equality or near-equality in the lengths of too (or more) cryptograms.
Isologs, no matter hear the cryptographic treatment varies, are among the
most powerful media available to the cryptanalyst for the successful
solution of a difficult cryptosystem — and, in some cases, may provide the
l4l
REOTIUCTED
-• r -
REF ID: A5 68 95
- RESTRICTED * ■"
only possible entries into a complex cryptosystem. An inkling of the
help afforded by isologs was revealed by the example contained in sut^’oT
6ld above; however, a much more striking illustration is given in the
next few subparagraphs. -
b. The following two cryptograms, suspected to be isologs, are
available for study: ... , . *,♦-
Message "A"
82265
8 0 2 7 7
6 3 6 2 9
8 17 13
38728
89697
2 8 12 0
9 0 8 7 0
46729
6 3
1
r if
0 3
■ 7 4 ' l 3
9
6
9 8 4 2
8 9
i
0 6
..9 4
0
0
0
, 1
3828
3 3
9
l 8
4 3
1
5
8
8
1 0 4 8
5 2
5
3 8
7 3
3
0
9
2
0749
9 1
1
4 7
9 9
9
2
6
4
14 6 8
9 3 8
1 6
5 1
7
5
0
_5.
.7 0 7.. 4
2 7 7
3 0
3 l
1
9
9
7
9 9 6 2
4 0
867
4 6
5
9 4
1
9 8 5 5
3 6
2
4 5
3 2 5 2 9
5 4 0 8 2
2 6 4 5 8
61752
13 3 6
118 0.
2786
1 0 C 2
5
.4
5
2
7 0 115
4 0 0 6 5
5 0 3 9
6 4 7 6
3881 .
3 2 5 5
0653
2987 .
Message "B”
3 0 15 0
4 5 6 4 7
90628
3 5 19 9
3 8 4 6 3
26121
0 6 4 8 k
4 4 10 5
59682
87497
9 9 18 1
7 7 5 3 6
9 0 13 8
1 7 5 4 7
83878
3 2 10 3
5 2 9 0 -0
4 6 2 5 3
14 5 11
6 9 6 7 2
2 0 3 5 1
9 9 9 7 4
1 4 6 4 8
9 4 8 8 9
9 8 7 1 5
5 9 7 2 8
97360
5 3 8 8 9
0570
0 2 3 2
0 6 4 6
3 7 2 8
2662
2855
4 9 6 7 6
41563
89277
0 4 1 1 5
8 5 8 6 4
112 7 2
80760
87300
5 0 1 6 6
25203
7 5 0 1 1
89216
5 3 8 9 8
2 0 5 0 4
89880
70893
On the possibility that some diname system (or systems) is involved, the
messages are written under each other in dinomes to facilitate the exam-
ination of the* similarities and differences of such a grouping of the
cipher texts, as sftown on the next page: 11
-*• iv. - . *■ ; • .
_ _ » » # * * *
1 . ' j r -3 - a '• - "* r-
fc* ‘ 1 * L. t *1 f *
« ' ; * ■; > -
- *;• ,■'-*< • I
- ‘ -
- ./ * ' e “ ' -
* m ‘ w t A
_ , .if % t «*
- RESTRICTED
142
t » k
REF ID : A56895
RESTRICTED
1
*■
•
. • <
■'5
10
15
A
82
■26
56
31"
03
74
83
96
98
42
32
52
97
01
15" "
A*
3°' '
■15
08
74
97
14
51
19
73
60
49
67
65
01
06
« i 1 - I
' B
80
27
78
91
06
94
00
01
38
28
54-
08
24
00
1 ^ J
65
B *
1 15
64
79
91
81
-i— .»^i k
' 69
t ■!
67
25
38
89
4l
56
32
52
03
• *j » ' 1 -
’ C
63
62
93
39
18 '
43'
15
§8
10
48
26
45
84
50
39
O'
9°
62
87
75
36
20
35
11
05.
70
89
27
77
50
11
1 1
* -
“
1 ii. i
1 "■ 1 r
i ‘ * . .
" ' # >“*, rt J** * -
D
81
71
35
' 25
38
73'
'30
92
07
49
61
75
21
64
76
D’
35
19
99
l oi”
38
99'
97.
• « k
45
02
32
o4
11
58
92
'16
*r^ *
38
72
89
11
47
99
92
64
14
68
13
36
53
38
81
' '"-fV
38
46
31
75
K..
l4
64
8°
06
46
i.*:t 1
85,
7
86
45
■38
- j\
98
f t r *
TlU t
• F
89
69 J
79
38
16
51
75
05
70
74
11
80
44
32
55
F»
26
12
18
38
78
94
88
93
37
28
11
27
22
05
04
.. ‘
28
12
02
77
30
31
.19
97
99
62
27
86
56
06
53
• G*
06
48
*4-3
21
,03
98
71
54
26
6?
80
-76
08
98
80 .
f 1 !
H
90
87
04
08
67
46
59
4l
98'
55
10
82
"22
29"
87
H’
44
10
55
29.
00
59
72
82
28
55
87
30
07
08
93 -
J
46
72
93
62 ■
45
_ ; ,
, * -
vv,-
",
A J, .
| » a
59
68
24
62
53-
•
L
-
-
f
- r
1 ’ * 1 J
li-IJj' \ '
»• »»*> 1 f "P V
..Sul i t, i » ’ : ' — - j^. lf «
The dinome distributions for the two messages
are
0 12
"nr. * «T‘
3 ^
5 6 7 8 9
0 12
. . ..
as follows:
3 4 5 6
r :jy:
i <
. . ./ti
8 -9
0
2
2
1
1
1
1
2
1 .
2
• 0
1
2--
l
2‘
2
2
3
1
3
-
1
2
2
1
1
1
2
1
-
1
1
1
l
4
_r
-
2
1
1
-
1
2
2
-
1
1
-
1
1
2
2
2
1
2
1
1
1
-
1
1
2
2 .
2'
1
3
2
2
2
■M ■-
*»
1
1
5
2
• 3 1
2
l
2
-
» -
2
1
1
5
-
4
-
1
1
1
1
2
2
1
.1
_i
4
-
l
- ,
•1
1
3
2
1
1
1
5
1
1
1
2
1
2
2
-
-
1
5
1
1
1
1
1
2
1
-
1
2
6
-
1
3
1
2
.1
-
'1
i T
1
6
1
-
3
»
2
1
-
2
1
1
7
1
1
2
1
2
2
1
1
i s
1
7
1
l
1
1
1.
2
1
1
1
1
8
2
2
2
1
1
-
1
2'
1
2
8
3
l
1
-
-
1
1
2
1
2
9
1
1
2
2
1
-
1
2
2'
2,
9
1
l
-i
_2
-1
-
-
2
3
2
■ * . %
Distribution for
Message "A"
Distribution for
Message "B"
* '*«- k
" -5" .
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•+ A-
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REF ID: A5 68 95
REBTRICTED
,‘T'
c. Since a general absence of marked crests and troughs is noted' “in
both distributions, if the division of these cryptograms into cLinomes ,^s
coiTecf , and if they are both monoalphabetic , it is quite probable thaV‘
some type of vai’Iant system (or systems ) has been used. With this in
mind, the encrypted texts and their distributions are scrutinized further
for some indication of the kind of. relationship which exists between the
methods of encipherment of the two messages. The distributions are seen
to be strikingly similar, not only with respect to the location of the
one predominant peak in each, but also in the close correlation of the. ^ 4
locations of the blanks in each.^T Furthermore, upon examination of the
superimposed messages themselves, it is observed that there are several
instances wherein a value in message "A" coincides with the same value
in message "El" (e.g., see positipns a/A' 3.4, b/b* 9)? This observation,
taken in conjunction with the marked similarity of the distributions,
strongly indicates that not only has the same general cryptosystem been
used for the encryption of both messages, but .that the same enciphering
matrix has been used for both. Also, in the case of the values 3& and
6 2, it is noted that wherever either occurs in one message the same value
| For the benefit of the s tudeht with a mathematical background, it
might be interesting to point out certain applications of cryptomathe-
matics in connection with these two distributions . E'irst of all, each of
the two distributions is much flatter than that which would be expected
for a sample of 125 dinomes of random text; i.e., a drawing (with replace-
ment) and recording from an urn containing equal numbers of counters in
each of 100 categories labeled 00-99 consecutively. In other words,
whereas "random" follows a characteristic distributional appearance, ap-
proximated by the normal or binomial distributions, the samples at hand
exhibit phenomena even flatter (or "worse" ) than that expected for ran-
dom, approaching the theoretical (and fantastically non-random) "equi-
librium" of exactly the jame number of tallies in each cell of a distri-
bution. The following tabie gives the observed number of x-fold repe-
titions in the two distributions, together with the expected number of
x-fold repetitions in a sample of like size of random text, which expected
number has been computed from tables of .the Poisson exponential distri-
bution (see Military Cryptanalysis, Part III);
-
Observed
Observed
-
X ■
Msg. "A"
Msg. "B"
Expected
0
17
29
1“
51 *
52
36
2
33
23
22
3
1
6
9
4
-
1
3
5
1
1
1
It is to be noted that in the distribution for Message "A" the observed
number of blanks (l*t) against the expected number of blanks from random
text (29) represents a sigmoge or standard deviation of 2.78 <r , which
RESTRICTED
Ihh
■ .(
r t!
,J*EF ID : A56895
occurs ^ t pfi othp£ n^ggoge, a phenomenon explainable on . the assumption .
that ijhe giaiulexb equivalents^ of these.'values are 'of such. low, frequency
that ho variant* values fiave Wen r provided for "these pla'intc'xb'' letters in
the cryptosystem.
d. With the foregoing details determined, it is now realised that
it should he possible to form, between the two messages, "chains" of
those cipher values which represent identical plaintext letters, a.s . >
exemplified below. Beginning with the first value’ in each message, 82 ■
and 30, a partial chain of ’ equivalent variants is started; ! now’ locating
some other occurrence of either value elsewhere (e.g., 82 at position H'8),
and noting the cipher value, coinciding with it (in this case, hi), the
partial chain maybe extended (including now 82, 30, and hi). After this
particular chain is extended to include as many values as possible,
another chain is formed by starting with any value which has hot already
been included in the preceding chain, this procedure being repeated until
can be translated as odds of 368 to 1 against its occurrence by pure
chance. Likewise the other entries besides 0 (in particular, the x-values
of 1 and 2 , and the cumulative, .values of 3 -and-better) may be evaluated
in terms of sigraageS', ' and the conclusion would be reached that the tiro
distributions have a most remote chance of being as flat as they are
r J}hrotv;h mere chance; foy instance * it is 3*05 <r or 877 to 1 against dis-
' "Wibuhion* "A", having only two 'tallies occurring three or more times when
13 such tallies" are .expec be<| Ipy random- -and this s igniage when taken into
consideration* with that 'of the number of blanks yields a sigmage of h cr
or approximately 31,000 to 1 of occurring through sheer chance, The sUrn.
total of all the deviations could be collectively evaluated, but this
would involve the laborioufc "computation of a multinomial distribution.
Since the distributions of the two messages are much worse than would
even be expected for random chance, the conclusion is drawn that the
dinoroe grouping is highly significant and therefore must be correct, and
furthermore that the cryptosystem involves, variants in sufficient numbers
for the plaintext letters to permit the_ encipherer to select the cipher
equivalents with a view to. suppressing as much of the phenomena of repe-
tition as possible. Secondly, the x test of the. 'two distributions gives
a % value of 206, as against the % value of 156 fpr random samples of
this size; this represents a sigmage of . 4 .02 cr , or a ratio of 33,000 to
1 against its happening "by, pure ^chance ^ i .e . , if the cryptograms were not
in the same general system ( and’ specific keys .“ Therefore it is a foregone
conclusion statistically , that not. only do the cryptosystems involve di-
nomes as the ciphertext grouping^ "but that the identical cryptosystem is
^ iiivolyed ^n the^.twq^ messages;, and that because of the close correlation
of th,e patters oj^he^ two ri distributions' , there is a good probability
that the cryptograms contain identical plain "text* and therefore are iso-
logs. This- specific illustration of the potentialities of cryptomathe-
matics indicates “the important role that this branch of science may play
in the art of cryptanalysis.
1 T p * 1 * - «
REF ID: A5 68 95
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all possible chains are completed. It is found that the following chains,
arbitrarily arranged here according to length, may he derivecl from the
two messages:
(06 l 4 15 2 6 28 31 35 73 7 1 '- 8i 89 98 99) '
(02 07 20 22 43 44 6? 90) ■■ - ...
(12 37 48 51 69 70 83 94) - <-
(03 30 4 l 54 65 82 97 )
(05 10 2l| 32 49 87 93 ) •
(16 18 36 76 78 79 86) .
( 27 '45 53 64 80 92) -
(11 39 75 88 ) - - —
(21 58 77 84 )
( 4 b 59 68 72)
(00 52 67) .
(04 55 6ij .
(08 29 56)
(19 71 96 )
(01 25) .
(13 85) .
(42 60)
Single dinomes:'
( 38 ) ( 47 ) ( 50 )
(62)_ (?l)
If we now make an arbitrary assignment of a different letter to represent
eaph chain (and each single dinome) and convert either of the messages to
uniliterai terms by means of these arbitrarily-assigned values, we note
the pattern of the opening stereotype "KEFEIffiNCE YOUR MESSAGE.....”, and
quickly recover the plain text.
e. The plaintext values when inserted into a 10 x 10 matrix having
arbitrarily-arranged coordinates yield the following:
-
0
1
2
3
4
5
6
7
8
9
0
u
M
T
R
p
0
E
T
F
-
1
0
D
N
H
E
E
A
-
A
c
. 2
T
I
T
-
0
M
E
S
E
F
3
R
E
0
-
-
E
A
N
B
D
4
R
Y
T
T
S
L
V 1
N
0
X
N
U
S
R
P
F
I
L
6
Y
r
W
T
S
R
-
-u
L
7
IT
c
L
E
E
D
A
I
A
A
8
3
E
R
N
I
II
A
0
D
E
- ■ 9.
T
G
S
0
N
-
C
R
E
E
Manipulating the rows and columns with, a view to.uncQvpring some^ symmetry
or systematic phenomena, the latent diaconal^ pattern" of "the ^equivalents"
_ f ir
' ■ * ‘ 9 J1
REF ID: A5 68 95
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T* _ », -t-\
w» i in^,»
' ; p *
for , car tain of .the letters (such as Ep, Np, Op, Rp, and Sp) is revealed,
and the ,rowg and columns of the reconstruction diagram are permuted to
•yield the following original enciphering, matrix:. . x
r - ^ r * * *
Z i *1 1 r .
•PV'jjfC r ■ : T v
j.;- ’ jf'
-* 1 ": ,f r »
i y i 1 *1.1
- - j
.6
8'
« | # r l
9 i[
<-■
5
h
£ TC*
3 7
.5
2
I
A
A
A
C
D
E
E
I
L
If
A
A
C
D ■
E
E
H
K
N
0
A
B
D
E
E
n
J
"H
0
R
A
D
E
E
H
I
If
0
R
S
C
E
E
G
I
' N
0
R’
' S’
T
E
E
F
I
M
0
Q
'S
T
T
E
F
’ I
M
0
P
R
T
T
U
F
I
L -
N
P
R
's’
T
‘ U
X
I
L
N
P'
R
S
T
U
tf ’
’Y
L
N ’
0’
s
S
T’
T*
V
Y
Z
7,
T
’3
’8
‘9
2
"i v ,v i Jrrrj 7 ~ 'y**
j lAi 1 . Mn: • f.J.- g
■ - -*«** *-« ■ sr.7 j/Jf •
,*r -,w: • • j*- ?
"There are' hb oh^serjrahle. relationships JL’n or between the sequences of
digits in ^he'Vo^l^^d^olxMn, cobrdiria^s’/^therefore for want of "any
visible phenomena 6lF further informatio n on the ’derivation (if any) “of
'■ 'the We digits, it i^asSunbcL that they mUsb ha^e been assigned at ' fandom.
The student will note* 1 that’ the' final matrix is identical - to that of
Figure 39 in paragraph 59 • •.*» /’**•- / •
f . It should be emphasized that in the example of the preceding
subparagraphs it was only passible bo form chains of values from both
messages reciprocally beqause the same enciphering matrix had been used
for both.. A non-reciprocal .chaining procedure would have been' required
if only the general system had been the same for both but the enciphering
matrices had differed in some respect, or 'if two completely different
variant systems had been used 'Te.g., one using a frequential matrix and
the other involving a. less -complex type of variant matrix, - such as Fig.
29). Specifically, it would have been lieqessary to maintain two sepa-
rate groups of.' chains , . one ’ grqup Tor each message j otherwise heterogeneous
values would have become intermingled.’ ■
g. Although .fin analysis of but one isolated example by means of
isologs was presented, the '-student should be able to appreciate the
significance and potentially enormous value - of lsologs to a cryptanalyst.
This value goes far beyond the simple variant encryption in a monoalpha-
betic substitution system: isologs produced by the use of two different
code books, or two different enciphered code versions of the same under-
lying plain text, or two encryptions of identical plain text by two dif-
ferent "settings" of a cipher machine, may all prove of inestimable Value
^-n the attack on a difficult cryptosystem.
/ ’ ' ' . j .
* » -* - *
i4t
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63 « Further remarks on variant systems . — a. A few words should
added with regard to certain subterfuges which are sometimes encountered
in monoalphabdtic substitution with variants,' and which, if not reco'gSJi
rfized in time, cause considerable delays. The considerations treated
"before in subpars . 52i and on the disguise of the length of the "basic
multiliteral group apply equally here to multiliteral substitution with
variants ; thus , in dinome systems , a sum-checking digit or a null might i
"be added in specified positions of the group to form a trinome. In
complex variant systems, the presence of a null as one of the digits Ojf
a trinome would add greatly to the complexities of cryptanalysis of that
system. "The most important of the subterfuges have to deal with the use
of nulls which are of a different size than the real cryptographic units,
inserted occasional] y to prevent the cryptanalyst from breaking up the
text into its proper units . The student should take careful pote of the
last phrase; the mere insertion of symbols having the same characteristics
as the symbols of the cryptographic text, except that they have no mean-
ing, is not what is meant. J^his class of nulls rarely achieves the pur-
pose intended. What is really meant can best be epcplained by an example.
Suppose that a 5*5 variant matrix with the row and column indicators
shown in Fig. 46 is adopted for encipherment. Normally, the cipher units
would consist of 2-letter combinations of the indicators, invariably
giving the row indicator first (by agreement).
V G I W D
A H P S M
T 0 IS B N
F U R L C
J T
v,a,t;f
A
B
C
D
E
G,H,0,U
F
G
H
I-J
K
I,P,E,R
L
M
N
0
P
W,S,B,L
Q
R
S
T
U
D,M,N,C
V
W
X
Y
Z
. L r «>l
Figure *l6
The phrase COMMANDER OF SPECIAL TROOPS might be enciphered thus :
COMMANDEROP . . .
VI EB PH IU FT IE AB TH WO "FW GT ...
These would normally then be arranged in 5 -letter groups , thus:
V I 13 13 P II I U F T 1 E A B T H U 0 P W G T . . .
140
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'REF ..ID : A56895
b, XI v 111 Ijc noted, however, that only 20 of the 2 <j_ letter;.; of the
alphabet have boon employed as row and column indicators, leaving J, K,
q, X, X, and !*. unused. flow, suppose these six let Lera arc used nr, nulls,
not in paivn , bu t ns Individual let lore inserted at random Just before
the real text is arranged in 5-lettcr groups . Occasionally, a pair of
letters might "be inserted, in order to mcislc the characteristics of
" avoidance” of those letters for each other. Thus, for example :
V I E X B PIIKIU FJXTI EAJBT MWOQP tt G K T Y
The cryptanalyst, after some study suspecting a biliteral cipher, pro-
ceeds to break up the text into pairs :
VI EX BP Hi IU FJ XT IE AJ BT I'M OQ FW GK TY
Compare this set of 2-letter combinations with the correct set. Only 4
of the 15 pairs are "proper" units. It Is easy to see that without a
knowledge of the existence ~of the nulls— and even with a knowledge, if
he does not knew which letters are nulls — the cryptanalyst would be con-
fronted with a problem for the solution of which a fairly large amount of
text might be necessary. The carcrul employment of the variants also
very materially adds to the security of the method because repetitions
can be rather effectively suppressed.
c. Similarly in the examples under paragraph 58, the letter J in
Figs. 27 and 29 may be used as a null; the letter Y in Fig. 28; and the
digit 0 in Figs. 33 and 34. . In Fig. 30, any letters in the range of
P - Z might be used as nulls, but this usage might be weak because of the
extremely low frequency of these letters as compared with the letters
A - 0; this is an important point to consider in the examination of en-
crypted text for possible poor usages of nulls . "
d. From the cryptographic standpoint, usage .of nulls in the manner
outlined above results in cryptographic text, even more than twice as long
as the plaintext, thus constituting a serious disadvantage . From the
cryptanalytic standpoint, the no' -ing of the cipher units in the system
described in subpar. b abo^e. constitutes the most Important obstacle to
solution; this, coupled with the us ■>, of variants, makes this system con-
siderably more difficult to salve ,
.espite its mono,alphabeticity.
NATIONAL SECURITY AGENCY
j
r
1
COURSE
IN
MILITARY CRYPTANALYSIS, PART I
NOTICE: This document contains information affecting the national defense
of the United States within the meaning of the Espionage Laws, Title 18,
U.S.C., Sections 793, 794 and Title 50, U.S.C., Sections 46, 46a and 46b.
Its transmission or the revelation of its contents in, any manner to an
unauthorized person is prohibited "by law.
National Security Agency
Washington 25, D. C.
1
December 1952
RE S TRICTED
REF ID: A5 68 95
♦
(BLAMK)
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REF ID: A5 68 95
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■ COURSE . E'T MILITARY CRYPT AtTALYS IS , PART I
Monoalphabetic Substitution Systems
Introduction
This is the first of a series of six basic courses in the art of
military cryptanalysis. The purpose of this course is to impart to the
student the methods and techniques which form the basis for the crypta-
nalysis of the simple types of military cipher systems. An understanding
of these principles is necessary to grasp the more advanced cryptonalytic
techniques employed in the attack on the complex cryptosystems which
constitute present-day military cryptography.
The scope of this course is: fundamental principles; unillteral
substitution; multilitoral substitution; polygraphic substitution; and
miscellaneous monoalphabctic substitution systems. It consists of ten
lessons and an examination as follows:
Lesson 1, Fundamental principles
Lesson 2, Uniliteral substitution with standard and mixed cipher
alphabets
Lesson 3 , Multiliteral substitution: miscellaneous matrices;
Baconian and Trithemius systems; elementary Baudot systems
Lesson 4, Multiliteral substitution with variants
Lesson 5, Polygraphic substitution; small matrices
Lesson 6 , Polygraphic substitution: quadricular tables
Lesson 7 > Polygraphic substitution: miscellaneous systems
Lesson 8, Miscellaneous monoalphabetic substitution systems;
concealment systems
Lesson 9 , Monoalphabetic substitution with irregular-length cipher
units: monome-dinome systems; miscellaneous systems
Lesson 10, Syllabary squares and code charts
Examination
The text reference for this course is the National Security Agency
publication, "Military Cryptanalysis, Part I" (December 1952).
This course has been designed as a self-study or extension-type
course; therefore, there is no limit placed on the number of hours that
may be spent in the completion of the course, any lesson, or the examina-
tion. However, for statistical purposes it is requested that the student
indicate the number of hours spent in the completion of each lesson and
the examination.
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3
REF ID: A5 68 95
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The cryptograms in this estcrse have for the most part been arranged
in proper worksheet form, obviating the necessity of recopying; and
frequency distributions have been given to reduce the amount of time spent
on the purely “clerical labor incidental to the solution. The underlying
texts of the cryptograms comprise hypothetical ground, naval, air, and ,
general administrative messages , Where necessary for solution, the
specific nature of the text of any particular cryptogram Is ‘ indicated.
Otherwise, the text of a message may be assumed to be general **
administrative or ground text.
■ .
The only materials required are cross-section paper of -j^-inch squares,
and a set of printed and blank alphabet strips. An eraser is of the ut-
most importance.
Special Instructions
So far as is practicable, detailed work sheets which usually form
a part of the solution should be submitted with the solutions . In all
the lessons of this course, it is required that the student recover all
cipher alphabets, cipher tables, and specific keys used. He will also
be required to state the method of operation of each cryptosystem and
give the key words upon which each component is based.
✓
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Oecurlty Information
NATIONAL SECURITY AGENCY
Washington 25, D. C.
COURSE
LESSON 2
TEXT ASSIGNMENT
1. a. What is the first step one should take in attempting to solve
an unlcnown cryptogram that is obviously a substitution cipher?
b. If this step is unsuccessful and the cryptogram is obviously
monoalphabetic in character, what type of cipher alphabet may be assumed
to have been used?
2* a* Name two methods of solving monoalphabetic substitution
ciphers involving standard cipher alphabets*
b. In the solution of a substitution cipher by completing the
plain component sequence involving reversed standard alphabets, what are
the successive steps?
c . Why do monoalphabetic cryptograms involving standard cipher
alphabets""yield such a low degree of cryptosecurity?
3* What are four characteristics of vowels which permit their
classification as such in monoalphabetic substitution ciphers involving
mixed cipher alphabets?
4. a. What two places in every message lend themselves more readily
to successful attack by the assumption of words than do any other places?
Explain* *
b. What is meant by the "probable word method" of solution?
5. a. What is meant by the word pattern "A B C B A D B"?
b. For each pattern given below, indicate one good English word
that contains the pattern:
(1) A B C B A D B
<2> A A B A
(3) A B C D A
Military Cryptanalysis, Part I
Uniliteral substitution with
standard and mixed cipher
alphabets
Sections V and VI
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1
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REF ID: A5 68 95
6. Solve the following cryptogram and indicate the specific
key (Apn6 c ):
J M Q V S
Q Z X I F
F M Z S L
I Z M L Z
C E M E B
F Q 0 M E
M D X Y Q
0 Z C Y Y
X J M Z I
V M Z I Y
0 Q W Y I
D K Y M V
M Z M N Q
E Q K M X
C C W Z B
0 Y I X I
C D Y Y X
C B Z Q I
F Z C Q N
H W D 0 X
ICDJQ
Y P M H D
Y M V M Z
M F S N Q
E Q K H N
Q D N E W
0 J M A W
IBEHD
X N M Y X
ZCSUN
Y X C B U
HQZME
C V'IDK
C W Z X Z
C C B Y X
C Z M Q Z
B C Y I X
I C D Y Y
X C B Z Q
F Y X 0 D
% |r _
^ _ S' ^
= - W
ABCDEFGHIJK I’M NO PQRSTUV V XYZ
<j>p=2655 <j) r =l?31 4*0*2636
7. Solve the following cryptogram, and indicate the specific key:
W X L M K
H R X K L
A T 0 X U
X X G H K
W X K X W
HEIKH
V X X W T
M H G V X
M H T K X
T P A X K
XIHUP
T K B G X
T V M B 0
B M R A T
L U X X G
K X I H K
M X W L M
H I T V D
GHPEX
W Z X X X
1
%
■ ^ ■ as -2
= “ ^ 2= g’ _ ■== = 2 ^ g
ABCDEFGHIJKLMNOPQRSTUVWXYZ
<t>p«66o
4>r«38l
<J)q«848
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2
REF ID: A5 68 95
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8, Solve the following cryptograms, and indicate the specific keys:
a. QHHYL YDWQJ JMEFC
h. YXSED YFSXU HWXUS
9« The following hadly garbled cryptogram was intercepted. Recon-
struct the original plaintext message, resolving the errors and omissions,
and indicate the specific key:
H
U
V
S
E
D
S
U
-
E
K
H
C
U
I
E
Q
W
U
D
K
-
R
U
H
0
X
H
U
U
U
Y
M
X
J
I
U
-
U
D
T
Q
J
u
T
E
D
U
A
Y
N
T
U
S
mm
mm
M
wm
M
I
J
E
F
Y
D
I
J
K
H
S
J
Y
E
M
I
0
Q
L
u
R
u
U
H
Y
I
I
K
U
-
J
E
Q
B
D
I
K
R
E
E
T
Y
D
Q
J
-
s
E
C
C
Q
-
T
I
J
E
Y
D
Y
W
Y
Q
J
U
K
D
Y
J
J
H
Q
Y
D
C
D
w
F
H
E
¥
H
Q
K
I
K
D
T
U
E
J
X
A
F
H
E
R
Y
I
Y
E
D
I
E
V
F
Q
H
Q
M
H
Q
U
X
J
E
E
V
—
F
«■
S
Y
Q
B
T
H
T
U
H
I
D
M
C
R
U
H
I
Y
T
= ^
^== e % ^
l£i= Sfjllgs mf __=5l£ is
ABCDEFGHIJKLMHOPQRSTUVWXYZ
<J>ps2270 <j) r ai311 <t>0«2136
RESTRICTED
3
- RE S TRICTED
!
REF ID : A56895
10. a* Construct a triliteral frequency distribution shoving one
prefix and one suffix of the letters of the cryptogram below* On the
work sheet below, Indicate by underscoring in black all repetitions of
three or more letters • Other significant details may be marked in
different colors;
b. Prepare a condensed table of repetitions of digraphs and
trigraphs""appearing more than twice, and include all repetitions of longer
polygraphs •
c* Using the data obtained in a and b above, complete the
solution of the cryptogram, and recover all keys «
5
A
B
C
D
E
F
0
H
U B S Y B
U X X P Z
P B Z H I
V G H 0 P
N P U X P
Q P P X P
B M G V V
C Z A H B
10
V X R P R
XBNBH
Z U X G L
P A B A Z
B Z V X P
DQZQF
GPHVH
U V B 0 B
15 20 25
C G U M Z
I G V R P
L B U I B
U B Z P N
C D U B B
G R U B R
B D Z X G
Z X P B U
X G P H P
R V X U Y
MQLZR
B C G H B
REGLL
P R R Z G
H B E B R
R P R A G
C U B Q P
R X G H D
B MB R X
M G L B V
B V X P Q
V V Z R R
Z Y V B P
XGPHV
if-
RESTRICTED
REF ID: A5 68 95
11* Solve the cryptogram below, suspected to contain the probable
word "BLOCKADE" j recover all keys*
5 .
10
15
20
25
LCTOE
LUZOD
UGREA
VZUSR
F Z X D Y
DRTLD
S D R Z S
D E U C M
UZZEZ
U D C D V
T Q T X D
A 0 Y Z C
Z W Y D X
JP T V Z D
■S CMZZ >
R Z A Q L
LDE C M
JURXB
TLCMT
L W Z Z R
ZS3ZX
0 Z V L C
_D 0 U D X
JZCET
UUTHZ
S U D A D_
E U F Z L
L Z Y L X
D R 0 N R
E Z LCD
HTUT1
L M D L C
eyzlm
D tJ Z 0 D
LHCED
BLTR7
MTLVT
A I E Z V
U T E Y Y
S R Z L X
g ggg— —
ABCDEFGHIJKLMNOPQRSTUVWXYZ
4>p B 2655 <1**1532 4 > o *27T0
5
REF ID : A56895
12. Solve the following cryptogram, and recover all keys*
EL W H E D Z VHJPJ ZHJLP JXBKV JLTWM
F W H WED WHW DM WSWDW J R E X I TKZCE
G KDJPW DCEMW DOKZH JJEPJ JPSB
HLKVFEH W J W E D H NZHJ E X X P W VJEND
HJEFS EDXWV OPJWE DVZQK ZHJZT
_gg
ABCDEFGHIJKLMROPQRSTUVWXYZ
<^pa3362 <*=19^0 4 q S 356o
6
RESTRICTED
REF ID: A5 68 95
13 • Using the sequences recovered in Problem 12, solve the following
cryptograms and indicate the specific keys:
a. URJJR XQUQX KSARB BET 0 1
ABCDEFGHIJKLMNOPqIsTUVUX. YZ
4>p S 25 4**15 4> 0 *l6
b. F D L D Y XZUMU E U F P H DVOFE ALYRW
UHL JX AFDYE X E K Q P DOYCV R E U A X
ABC DEf GH I JKLMHof U S TUVUXYZ
4>psl63 ^r®9^
l4. The following cryptograms, enciphered with random cipher
alphabets, are in bona fide word lengths. Solve them.
a. HY ARV JZGHAROT VK CGKMMGKHZM LKUG
LKUG 0 R 0 6 SOZ SMVHFSRMJROT
i
JEHZPUHGVEGM RO MCJKKSJKUME
b. RGRQRU TDBPYURDP ZFTAVDRC AYCFO
JO DRZYUUFSPPFUZR TFADYGP
c. CDGWDSA LCAUMMDOR BUCD YV DVD JR
IYSUAUYVS' 1/ Z C *Y S S OUTDO
RESTRICTE D
7
REF ID: A56895
RESTRIGTEB -
15* In solving several unrelated monoalphabetic cryptograms t the.
following cipher alphabets were reconstructed. Recover all key words in
each case. To facilitate solution, significant segments have been
underlined.
Q> •
P: ABCDEFGHIJKLMNOPQRSTUVWXYZ
0: If L W PFRTHSYDQ A K V EBMXGCOZ I J U
b.
“ *
P: ABCDEFGHIJKLMNOPQRSTUVWXYZ
C: Z Q X P E ONM W LKJHGF DBVYUTRICSA
c.
Pt ABCDEFGHI, JKLMNOPQRSTUVWXYZ
CiPQERVMOZWUTHAX BCD F S Y G I J K L N
d.
P: ABCDEFGHIJKLMNOPQRSTUVWXYZ
CiAUZJTXHSWGRMBN PCI Q F E K Y P D V L
e.
P: ABCDEFGHIJKLMNOPQRSTUVWXYZ
CiCKY E B 0 Y F D P Z G Q H S ITLWNJURAMX
f.
P: ABCDEFGHIJKLMNOPQRSTUVWXYZ
C: LM CPOQI_JHR_SNTBD_EUGVKA W X Y F Z
£•
P: ABCDEFGHIJKLMNOPQRSTUVWXYZ
C: C D G P V Z K H Q L A E I J N S W U B F M 0 T X Y R
h.
P: ABCDEFGHIJKLMNOPQRSTUVWXYZ
C: LBEKDGRMFA X S N H C Z T 0 I Y U P J V Q W
RESTRICTED
8
I
RESTRICTED" aecvurlly Information
NATIONAL SECURITY AGENCY
Washington 25, D. C.
COURSE
LESSON 1
TEXT ASSIGNMENT
1. a. What four things were thought "by, Captain Hitt to he essen-
tial to crypt analytic success?
b. What six additional elements are also highly desirable?
2. a. Define the terms "cryptology", ''cryptography", and " crypt -
analysis. 17
b. What are the essential differences between substitution and
transpos it ion?
£. Differentiate between a code and a cipher system.
d. Explain the difference between the terms "general system"
and "specific key" .
e. Distinguish between monoalphabetic and polyalphabetic
substitution .
3. What four fundamental operations are involved in the solution
of practically every cryptogram?
4. In the solution of cryptograms involving a form of substitution,
to what simple terms is it necessary to reduce them in order to reach a
solution?
5. Is it always necessary to determine the specific key in order
to reconstruct the plain text? Explain.
6. Indicate the language In which you would expect the plain text of
the encrypted portion of the following message to be written. Give reasons
for your answer.
From: Joao Fialho, Sao Paulo, Brasil.
To: Gualterio Costa, New York City.
Com referenda ao seu telegrama. NSM NRJPN INJ PMVCOCEN
VNPSN PMBMPGEN QMT JBCVCJ IJTJM DTGAJ LTMCPN KPJUCEMIVCNP PMHMQQN
UMIVCHMISJQ SMFVMCPJ SPCHMQSPM.
Military Cryptanalysis, Part I
i
Fundamental principles
Sections I -IV, inclusive.
1
REDTRICTED
REF ID : A56895
7. a. The letter E represents what percentage (in round numbers)
of the letters in English telegraphic text?
b, What are the four most frequent consonants in English tele-
graphic text?
c. What are the five letters of lowest frequency in English
telegraphic text?
d. What are the four most frequent digraphs in English tele-
graphic text?
e, Account for the discrepancies between frequencies of letters
in English literary text and English telegraphic text.
8. What three facts can be determined from a study of the uniliteral
frequency distribution?
9. In the following extract from a speech given during World War II,
each dash indicates the omission of a letter. Complete the text by
writing the necessary letters over each dash to form appropriate words.
"Washington’s Birthday is e most a p occasion
for us to talk with each about things - al they are
and things as we they shall be in the
"For t years. General Washington and his ________
^ ^ Army were" faced £ o _ with formidable""^
and recurring — — — — — — — ~ — _ and equipment were
lacking. In a every winter”* was — a — Valley Forge. Through-
out the states there existed selfish men, jealous •
men, u 1 men, who that Washington's
_ _ _ _ _" was hopeless, that he should - ask - f or an
peace. - — — — — — — — —
’ "Washington's in those hard has provided
the for all Americans^ ever since — a model "of — moral __-
_ ___ — a. - He - held to his , as it had been charted in - the
Declaration of Independence. — He and the men who __ _ ^
with him knew that no man's life or — was secure, "without"
freedom and free i — n - s .
"The present _____ struggle has us increasingly
that o m of - person and •£" of property anywhere
in the — depend upon the s'ecurity - of the rights and obliga-
tions of liberty and _______ everywhere in the world.
"This war is a new °f war . It is
from all other wars of the — — , not only in Its methods and
-RESTRICTED"
.2
REF ID: A5689
Tjub also in its geography* It is warfare in terms of
every c o n _ ^ . every a d, every sea, and every
a ^ ~ n e in™" the"* world. The ~ 3 Z Z Z oceanfl which have "been
S 11ZZZZ- the past as our ~ ~ Z Z _ from attack
Fave~become s s battlefields on“wSich"we are
— Z challenged by our enemies — — —
10* a* In the following examples the words Of sentences have heen
transpose's* Rearrange the words to make plain text*
(1) AT NOTHING REPORT THIS TIME TO
(2) ARTILLERY SECTOR BARRAGE NORTHWEST HEAVY IN
b* In the following examples the letters of several words of
each sentence have heen transposed. Rearrange the letters to make good
words that will give intelligible plain text,
(1) Eight SESTYODRER have DTPADERE to join SAKT REOFC
(2) ABELSKJ to contact ATTAUSBLO on my right AFKLN
c. In the following examples the words of each sentence have
heen transposed and, in the case of several words, the letters have also
heen transposed. Reconstruct the plain text*
(1) OLANG RIDGE TANK G3MN0V EHOTISL EAST NOMLCU
(2) DOWN MEYEN OFANERTON SIX THIS OTHS SNEALP
d. In the following examples, the letters of each word' of each
sentence have heen rearranged in the order in which they appear in the
normal alphabet* Reconstruct the plain text*
(1) ADELY AACKCT CDDEEHLSU OT CCEEMMNO AT EGHXT HIST GIMNNOR
(2) AUEEIIIMMTY NOHJ CEEIPRT ADHIRTWW 0T AADEEGNPRRR IINOOPST
e. In the following examples the plain texb has heen broken up
into groups of five letters and then in each group of five the letters
have heen rearranged in the order in which they appear in the normal al-
phabet. Reconstruct the plain texb.
(1) ORSUU ABB® AEHNS ENSUV ADKOR ADEGM EEINN EMNVY EELSS S
(2) AEIRR ACNNO ABfSS ADEPT ELORR OPRST AILRT EELRY ACLMP EEMNT
DESST DEORY
a
RESTItlCTEB -
REF ID: A5 68 95
11. Using cross-section paper prepare a uniliteral frequency tar
distribution of the letters of the following paragraph:
"The shortest and surest way to live with honor in the
world is to be in reality what we would appear to be?
all human virtues increase and strengthen themselves by
the practice and experience of them."
12. Determine the class to which the cipher systems, which were used
in enciphering the following messages, belong:
i *
a. 0 R A N A THPHO SKTCD MERES CERAE
R R U S A ETLGD AYECA
S’ 35 _ S=3= __
abcdefghijklmnopqrstuvwxyz
b. DHJJK QOAHR XKSOF H P Q G A PPHLA
DIADE EJROA MAHQA
—j. ass-. _
ABCDEFGHIJKLMIOPQRSTUVWXYZ
c. ROLEH KBWFZ CQCPZ NVJWZ M I V E Q
EPCIN OJSJU Y M W Q B
ABCDEFGHIJKLMNOPQ
13. Which of the following substitution
U J K L W
S E L Y R
M R Z A Y
K R W A P
E U V K L
X Y X B X
A 0 S G U
K 0 I E V
F S P A
J D A T
D C L G
A R 0 E
RSTUVWXYZ
ciphers are monoalphabetic?
Q PHTKR DZRGL
U
I
V
W E U Z G
0 E W J E
W S C W R
W F V X M
I F 0 K M
S B C Y X
ABCDEFGHIJKLMROPQ
RSTUVWXYZ
b.
1 U P Y P
S X X A Y
W U P J P
P J 0 P Z
X X A E P
P W K A S
0 B S H U
S V P Y S
A F G Z
LHPR
H U P G
M P 0 A
P V G L H A
H A L 0 B A
F X G K P H
X U L S L P
S L X H U
X P L V S
P V S W U
C G N J X
zx _ — ~ jlT H r: 2^ — — =r JiT
ABCDEFGHIJKLMROPQ
RSTUVWXYZ
k
RESTRIGTEB -
RESTRICTED
'REF ID : A56895
GXIVL
G M X L W
V H M X A
RTIYZ
Z X M X S
Q I V Z W
loth
K T 0 X G
L 0 Z G R
Q B R X K
TKM.X
A W X L Q
W E J L X
K T D V L
G B Q K Q
LOZGR
PWTKZ
M X A E X
L W Z X G
X V W G Q
5 S0 «
S- —* % %% S ^ ^ ^ ^
ABCDEFGHIJKLMNOPQRSTUVWXYZ
l4> The following messages were enciphered nusnoalphabeticaUy* Be*
tennine in each case whether the cipher alphabet used was a standard or
mixed alphabet and if standard, whether direct or reversed*
a*
ARTOR
L 0 V N Q
RLEZV
ZHREZ
W Z B
0 R
Z K Y L F
A 0 Z S 0
OIORF
P J Z P P
L D Z
D N
L R Z L B
L A B W Z
&HAPO
W Q H 0 0
R Z I
Z U
•
-*• -
5
ES
S — — -
E — —— %
5
0
A B C D E F G
HIJKLMNOPQR
s
T TJ V W X
Y
Z
b.
E S P A P
L V D L Y
0 E C Z F
RSDTY
-
E S T
D 0
T D E C T
M F E T Z
IBFII
V W J T 0
P Y E
T Q
J T E L D
OTCPR
E D E L Y
0 L Q 0 H
T A S
P G
0
IS
B?*'
B
%
e
ABCDEFGHIJKLMHOPQR
S
T U V W X Y Z
c.
PYHTt
X 0 L W Y
J J V Y X
0 I L Y R
YQYPJ
KRYLK
Y H Y L C '
P A Y A C
LYXIR
Q Y J V 0
Z K 0 X C
P C R E K
U K U P J
I U J U 0
P R I A S
mmm
i
5
s _
= — _ =
£
ABCDEFGHIJKLMHOPQRSTUVWXYZ
RESTRICTED
5
REF ID: A5 68 95
RE STRICTED
r
15. Derive the <j>p, A-g, A**, and Ao for each of the following
distributions, and evaluate the /oonoalphabetic7 goodness of <j> 0 and A 0
of each in terms of "good”, "fair", or "poor", entering these data in the
attached diagram* On the basis of the foregoing, decide which distribu-
tions are most probably monoalphabetic and which are most probably non-
monoalphabetic, indicating your decision by a check (y) in the diagram;
in the case of those not clearly belonging in either of these categories ,
check "decision suspended"*
3 § —3
a. ABCDEFGHIJKLMNOPQRSTUVWXYZ
b. 1 B C D E F 0 1 1 J K L fi 5 0 P Q R I 5 U V W X Y Z
£
c. A B C D E F 0 1 I J K L M N 0 P Q R f T U V W X Y Z
“ ggm •— mm 25 g-
d. ABCDEFGHIJKLMNOPQRSTUVWXYZ
e. ABCDEFGHIJKLMNOPQRSTUVWXYZ
f. ABCDEFGHIJKLMNOPQRSTUVWXYZ
3_=s _ W 3 sa -
g. ABCDEFGHIJKLMNOPQRSTUVWXYZ
h. ABCDEFGHIJKL MNOPQRSTUVWXYZ
Goodness Goodness Decision
of <|> 0 of A 0
H I +p I I $0 I Ap I Ar I M o|f|p g| fTp ®no.|gggo.|s«8p
a#
REF ID : A56895
RESTRICTED j - -
1 6 . From the intercepted traffic of three intercept stations oper-
ating in the same sector of the front, the following code messages were
selected for study by a member of the cryptanalytic section at GHQ* They
are undoubtedly three versions of one enemy message, but there appears
to be a number of differences, due no doubt to operating difficulties at
the several stations . Study the messages and reconstruct from them the
actual code text sent by the enemy station*
I. Time intercepted 1612 byHB W F F V LDC
GR 35 ST
NR
17
D
Y
B
I
E
D
U
F
T
0
A
M E
J
A
•K
I B 0
N
s
G
C
0 Y
F
0
B
A
K
D
0
D
L
A
L
U F
Y
D
K
AW A
L
A
P
A
Y N
C
0
D
A
P
K
E
D
TJ
R
J
0 P
I
D
J
E N 0
X
M
E
H
A Z
L
0
G
I
S
K
U
T
E
G
E
V A
V
K
I
P B E
M
K
E
H
Z A
H
0
B
W
E
A
V
D
U
Z
F
0 F
A
E
M C 0
Z
E
G
B
L 0
D
0
F
Y
0
E
N
C
-
-
M
AW
E
N
-
—
-
II.
Time intercepted l6l0 by
Mi
MR
M F F
V
L D C
1
t
GR
35 BT
NR
I_
D
Y
B
I
E
B
U
F
T
0
A
M E
J
A
K
I B 0
N
I
P
K
0 _
F
B
A
K
D
0
D
L
A
L
TJ F
Y
L
K
AW A
L
A
P
A
Y N
D
U
A
_ P
I
D
J
E N 0
X
N
E
H
A Z
L
0
G
I
S
K
u
T
E
G
E
V A
V
C
I
R B W
K
E
H
Z A
S
0
B
W
E
V
A
D
U
Z
F
0 F
E
T
E
M C 0
Z
E
G
B
L 0
D
0
F
Y
0
A
E
C
D
A
M
A W
E
N
°
M
E
M
C
0 Z
A
C
F
A
H
L
0
F
I
R
0
9 3
5
III
•
Time :
intercepted
1612
by YG
W F F
V
L D K
GR
BT
NR
17
D
Y
B
I
E
D
u
F
T
0
A
M E
J
A
K
S B 0
K
I
P
C
0 Y
Mi
A
D
0
L
V F
Y
L
K
A W A
L
A
P
E
T Y N
C
0
D
A P
K
E
D
U R
W 0
P
I
D
JEN
0 X
M
E
H
A Z
L
0
G
H
K U T
E
G
E V
A
U K
I
P B
E M
K
E
H
Z A
H
0
B
W
E
A
V
D
U
Z
F
0 F
E
T
E
M C 0
Z
E
G
B
L 0
D
0
F
Y
0
E
N
C
0
A
M
AW
E
N
M
AWE
N
E
X
F
0 M
E
M
C
0
Z
A
C
F
A
B
L
0 F
I
R
0
9 3 5
7
REF ID: A5 68 95
REF- ID : A56895
RESTRICTED
Securit y lufuiwatlon r
NATIONAL SECURITY AGENCY
Washington 25, D. C.
COURSE Military Cryptanalysis, Part I
LESSON 3 Multiliteral substitution with
single-equivalent cipher alpha-
bets
TEXT ASSIGNMENT Section VII
1. Solve the following cryptogram, And recover all keys:
5 10 15
A
DT
LR
WE
OE
0E_
WH
RR
WR
LA
WH
WA
DE
DA
WR
LE
B
t IE
OR
RE
WT
OR
WA
OH
WH
OR
LE
LR
WA
RR
RR
WH
C
WA
WH
OE
OR
LE
LE
WR
WA
WH
OH
LR
LE
LR
WA
OH
D
OE
LR
OA
OA
OE
LR
OR
RE
OA
OA
WH
WT
WH
WA
WA
E
^WR
WA
WH
DE
RT
OE
WH
WH
RE
OR
OA
RT
OE
LR
OR
F
RE
WR
WE
WA
OH
DE
WR
LR
WA
WA
WR
WA
WH
DE
DA
G
in
LR
WA
WH
OA
DE
LR
IT
IT
LR
OA
WR
DE
WR
LR
H
WA
OA
LR
RA
RA
LR
WE
OE
DE
RT
OE
WH
RR
WR
LA
J
. WH
WA
HE
DA
WR
LE
LE
OT
WH
OE
WH
WH
WA
RA
LR
K
OE
OH
WH
RE
or
DO?
OR
RE
RE
WR
DE
WR
LR
WA
OR
L
LE
OR
OE
DE
WR
LE
LE
WH
OE
DT
OA
WE
IT
IT
LR
M
OE
DE
OA
DE
LR
LT
OH
LR
LE
LR
WA
WH
LE
OT
WH
N
WA
WA
WR
WA
RR
(For distribution, see next page)
JL
RESTRICTED
REF ID : A56895
A E H R T
D 3 12 - - 3
L 2 13 - 21 5
0 10 14 6 10 3
R 3 7 - 5 3
W 22 4 22 13 2
:2270 (|> r =1362 <|> 0 =2288
(25-element alphabet)
2. This message was sent by the Fifteenth Infantry. Solve It and
recover all keys:
CY
AO
NX
CN
NO
CN
AO
AO
OG
ON
NO
BY
OX
OX
RO
CG
NY
RO
AN
RE
AG
RO
OX
AO
AN
AX
AX
AG
AN
AG '
CN
RO
OX
OX
BY
AN
AG
CN
BE
CX
BN
BX
CG
RO
ON
CO
RE
CN
AY
BG
CE
ON
NO
AO
OG
RO
NO
NO
RO
RE
00
HG
BY
OX
OX
RY
AG
AX
BY
AN
OG
CN
AO
OY
OG
NO
OX
CY
NX
OG
AO
AN
CN
AG
RE
AG
BY
OG
NO
AO
BO
AO
CN
CG
AG
CN
ON
BO
CN
AO
OY
CO
OE
ON
NO ,
OG
RO
NO
NO
RO
NO
AG
CN
RE
AO
OX
RX
AE
BY
AN
BO
E G N 0 X Y
A 1 9 7 12 3 1
Bill 316
C 1 3 11 2 12
N - 3 - 9 2 1
0 17 5 19 2
R 5 - - 9 11
4>p=960 (approx.) fcsluo <j> 0 =7l6
(36-element alphabet)
2
REF ID : A56895
RESTRICTED
3. Solve the following cryptogram, and recover all keys:
5 10 15
A
RG
GP
EE
GR
RG
GP
ES
GR
RG
PP
GE
PR
GE
RG
GS
B
AS
GR
RR
GS
AE
PP
GP
GA
PP
RA
EA
ES
GR
RG
PP
C
RA
PR
GS
RE
GP
AR
GP
GS
PP
GP
RG
RA
EA
PP
s
PS
PG
AR
PE
GA
RR
RG
GP
RR
RE
PG
PP
RA
EA
RS
E
PG
PE
EG
AR
PE
GA
RR
RG
GP
RR
RP
AE
GS
GA
AP
F
GP
PP
RA
EP
ES
GP
RA
GP
RA
PE
PR
PR
AE
GR
GP
G
RA
GA
GP
GP
RR
GP
RR
GR
AS
AS
GP
RR
GR
GS
PP
H
GP
AE
GE
RS
PG
RG
GS
RE
PP
GR
GG
GS
PP
GR
PG
J
OA
PG
RS
RE
PG
AS
PR
GS
GA
GE
RR
EA
ES
GR
RG
K
HR
RP
GS_
_PP_
_PP .
_GS
AE
GR
PG
GA
EP
RG
GP
EE
GR
I>
RA
GR
PP
GR
PG
GA
AR
GS
RA
RP
GP
GP
GA
GS
PE
M
ES
PG
RG
GR
ER
GP
RR
RP
GE
RG
GP
AG
GR
AS
GP
U
GA
PP
GS
AE
AR
PA
EP
RG
GP
PR
AE
GE
RG
GP
TO
P
GP
RA
PP
GP
RR
A
E
G
P
R
S
A
—
7
1
1
5
5
E
4
3
—
3
1
5
G
11
7
1
27
16
14
P
1
5
10
16
6
1
R
11
4
16
4
12
3
4 >ps 2260 (approx.) ^>=1164 ^ 0 =2294
(30-element alphabet)
RESTRICTED
REF ID: A5 68 95
RESTRICTED
4. Solve the following cryptogram,, and recover all keys:
5 10
3s A B
B
B
$ps499 4 r =277 $ 0 = 5te
(27-element alphabet)
5, Solve the following naval message, and recover all keys:
10 1
1
0 3
3 3
1 2 2 3 1
0 3 0 2 3
3 3
1 2
2
3 10 0 0
0 0 2
6
0 6
1 0
1 5 2 3 1
•
4 0 4 2 4
2 4
0 5
2
33206
0 4 2
6
1 1
2 2
3 3 2 6 3
1 2 3 3 4
1 1
0 5
2
33011
0 0 1
1
2 2
0 0
2 0 0 1 0
0 2 6 0 0
0 6
3 5
1
6 2 6 1 1
367
6
9 3
1 0
6 2 2 2 2
2 6 0 5 0
4 1
2 2
1
0 4 1 0 1
•
9 11
2
4 2
3 0
5 2 6 0 4
2 2 2 2 1
2 1
6 0
4
10 15 3
0 2 3
1
4 l
2 2
3 0 10 5
0 0 113
5 0
0 2
4
lllll
5 0 4
1
0 1
3 1
4 2 3 0 5
0 3 0 4 2
6 0
6 2
3
10360
RESTRICTE D
4
REF ID : A56895
&
I
restricted
b, Solve the following cryptogram, and recover all keys:
4 5 2 6 4
56282
02523
29276
1 6 1 4 5
23820
6 3 2 16
52729
27212
6 0 6 5 2
16729
47694
56529
0 2 14 6
0 4 1 6 1
2 5 4 2 4
90692
12 14 3
6 5 0 2 6
45672
92325
61272
8 4 5 ^3
0 4 1 8 2
0 4 2 2 1
6 7 2 6 2
9 4 5 2 3
4 12 5 2
9 2 9 4 5
23820
46272
34506
52921
63023
4 5 6 4 6
7 4 5 6 5
29082
21670
2 3 4 5 6
1 2 5 8 2
0 2 9 4 7
27650
29210
23^72
1 2 5 4 3
65000
7 * Solve the following cryptogram, arid recover all keys:
05105
23804
91161
3 8 '
3 4 9
22702
7 4 4 9 1
16138
33834
9 2 2 7 4
2 7
5 0 5
31612
7 4 4 9 2
16127
1 4 9 1 4
9 2 2 7 4
3 8
216
12724
91161
2 7 13 8
10523
8 4 2 7 4
05405
23801
6 1 4 9 l
16105
22713
80271
05227
44910
51052
0 5 3 2 7
1 4 9 2 1
6 0 4 9 1
0 5 2 2 7
10502
7 4 16 3
38016
11653
8 5 4 9 2
2 7 4 0 5
2 0 5 3 1
61494
49238
4 2 7 1 3
8 2 4 9 2
2 7 4 2 7
20522
7 13 8 0
49127
0 2 7 1 4
91270
4 9 14 9
12702
7 2 2 7 3
0 5 5 0 5
30522
7 4 2 7 2
16127
13814
93052
49449
24910
52380
0 5
1 4 9
23834
9 14 9 2
2 7 4 4 9
23823
8 2 3 8 4
3 8 10 5
2 3 8 4 4
9 10 5 0
5
RESTRICTED
REF ID: A5 68 95
8. The following is a text in the Baudot teleprinter code enciphered
hy a simple machine employing five two-position switches which operate
polarized relays. Each switch has the function of changing the polarity
of its respective baud (a single "mark" or "space" impulse), if the switch
Is in the ’active* position. If the switch is In the ’inactive* position,
the polarity of the baud is unaffected. The switch settings remain con-
• staat for each message. As an example, if switches 1 and 4 are active
(x), and 2, 3 and 5 are inactive (o), then the word ENEMY is enciphered
thus:
Key: xooxo xooxo xooxo xooxo xooxo
Plain: +«+«+ j
Cipher: — +- +-+— — +- +-+-+ --+++ j
i
Solve the message and recover the switch settings.
1
2
3
4
5
6
■ 7
8
9
10
A
+— +“
+-++-
+ + -+ +
+ ++ + -
+"•
MW
-+++-
”
B
+-+
*-
+ »—• +
-
-+++
++ +
++
+-+++
+++-
>+
+++-■*-
— +++
C
++ +
++++ +
— + -f
++-++
+ -+
+-
4-
-++-+
+++++
++--+
D
+++
+++
+- ■ +
++ !■++
+-
— +
— — •"++
++—
■+
+++++
E
+ +
+-++-
+ + +
*
+
+ +
—
+ - +
-++
+-++“
F
+—•*+
-•++ + —
++ +
I
1
+
+
+*
+
+
+
1
M*(aw n
+
+-++«
0
+++ —
+“■“+—
- + “ + ~
+++*+
+++-+
+
1
1
1
+
-++-
'+
+-+ —
-++ —
H
+-+— *
“ - +“+
+++++
+ +
+4
I
+
+
1
+
+++-
-
+ +
-+++-
J
-+
+
I
+
1
1
+
+
+ + +
— +4»
— H+
3:
+
+ +
t
1 —
- -
-
4:
+
+ —
1
4*
+
—
5:
+
- +
mi
♦
+
*•
++
5
l 4
T
3
1 6
1
•
+ -
1
5 -
8
4
l 13
1
2 • — +
-
3 4
3
1
3 1
2
—
2
- 5
-
2
-
3
<i>p=480 (approx.) <f>r=234 <|> 0 =386
(32-element alphabet)
iM SBTKlCTED
6
REF ID: A5 68 95
nEDTRICTECr
NATIONAL SECURITY AGENCY
Washington 25 , D. C.
COURSE
LESSON k
TEXT ASSIGNMENT
Military Cryptanalysis, Part I
Multiliteral substitution with
variants
Section VIII
1. Solve the following cryptogram, and recover all keys:
5 10 15
RA
BE
KE
PE
VE
TI
BO
LA
GO
DU
JO
BE
KI
BI
JO
BU
~JA
VA
ME
LA
BE
KI
RE
FE~
DO
VI
JO
SA
DO
JE *
KI
BA
MO
SA
CU
GE
GE
PI
BO
KI
JU
CE
Cl
MI
NE
FO
JU
CE
RE
NA
BU
BE
~K0
RA~
DE
KE
TE
SE
TI
JO *
' FA
GO
DU
DO
JE
KE
DI
JO
BU
Ha
CE
BO
FO
BA
BU *“
* DA
EE~
JO
NI
DO
NA
BO
BE
"PI
GI
ME
TE
CO
JO
TI
SA
BO
TI
DU
MO
FA
BU
NT
DU
DE
"TO
GI
BE
SE
BU
GE
CO
PA
TA
KE
CE
NA
VA
MO
LO
ME
NA
DU
DE
CE*
' BO
FO
DA
DU
"da
LE
BO
SI
JO
VA
DO
DE
~TI
NI
DO
CO
FI
DE
VE
Cl
BU
DA
Li”
BO
VI
DO
NA
JO
BE
"o
va"
DU
DE
”ko
GO
RE
MO
PE
SA
RA
JE
KA
DO
PI
RI
(For distribution, see page 5)
1
fMTinTmoftED
REF ID: A5 68 95
2. Solve the following cryptogram, and recover all keys:
5 10 15
A
DR
DD
SY
DA
RA
RR
SB
YA
BT
TY
AR
HI
DB
TB
AD >
B
YY,
YB
SA
AA
HI
DA
TD
HR
YB
TD
BB
RI
AI
HH
BT
C
DD
IA
AI
BB
HA
YD
TH
YA
HI
BA
YT
YD
YY
BD
YH
D
SD ,
5T
SB
AA
ST
YD
RH
SD
SR
YR
DT
SR
RA
RR
YB
E
SA
BT
TY
HR
AI
DB
IB
AD
DY
YB
SA
HA
HI
DA
TD
•
F
TS
DB
SH
YH
DI
SD
TT
TT
YY
HH
ST
YI
SB
AA
ST
G
X DD
AH
DH
YT
RH
HI
ID
AR
SB
BA
RI
HB
AI
HI
RH
H
DB
SH
HA
RI
DA
AI
IB
YB
DI
SI
DD"
YA
BB
YT
IS
J
II
YH
TY
BS
DD
YR
SR
RI
HH
TD
DT
TA
AI
RY
ST
K
SH
DH
AB
AI
TI
YT
AH
HY
AR
AI
RH
DI
YD
DD
YA >
I
' TB
~W
~hh
SB~
AA
DT
DD
RH
YD
“DR
YB
DH
SH
SR
DD
H
DA
SI
RI
ID
ST
BD
SI
SD
TT
BH
SH
RI
AA
HI
BB
M
IS
BI
HI
RH
AY
DB
BA
AI
DH
SH
(For distribution, see page 5)
•ft UUTlliCTED
2
REF ID: A5 68 95
ftEOTIUCTE e-
3. Solve the following cryptogram, and recover all keys:
5 10 15
A
B
C
D|
E
F
G
H
J|
K
L
M
K
P
1 — ...
99
18
57
82
12
28
78
90
25
oh
15
30
04
06
14
* 57
34
64
20
72
15
30
02
57
44
84
52
66
11
81
87
58
35
78
31
l4
70
90
68
47
30
13
15
21
86
92
43
10
30
35”
20
31
"32
64'
18
57
26
84
12
06 y
‘ 34
"25
69
72
90
"78
07
90
31
29
57
50
82
19
53
31
72
51
36
10
86
36.
47
18
67
26
04
92
82
30
08
31
58
90
88
87
91
10
20
82
31
~l4
56
57
31 V
*”88
04
31
30
66
47
30
36
18
99
~20
06
97
31
21
55
99~
18
20
10
28
74
68
90
~4l
69"
82
90
78
31
86
88"
15
91
26
92
72
87
”l4
43
20
53
28
64
92
47
02
58
35
10
96
05
34
37
85
oT
26
80
50
“92
68”
10
70
81
-92
18
02
86
49
47
07
82
94
06
69
15
21
90
56
10
40
01
68
190
15
35"
57
52
"32
60
47
64
36
71
06
55
00
68
|78
45
52
12
69
43
(For distribution, 6ee page 5)
KESTRICTED
3
REF ID: A5 68 95
l
RESTRICTE D .
4, This message is suspected of having an ending similar to Prob-
lem 3* Solve it and recover all keys:
5 10 15
1
,_LJ 1 rnf
r ‘
Jm
~ r Fil F
""""
n r "~
A
1
22
“oT
71
29
"l9
"83
05
"34'
76
58
¥
56
62
26"
22
B
35
48
75
13
78
58
34
65
02
07
71
51
87
35
96
C
10
32
69
45
47
81
46
11
01
l4
67
37"
75
79
35 *
D
*15
53
29
37
46
60
19
30
94
66
49
68
88
57
98
E
• 84
93
30
86
28
90
51
o4
53~
03
84
76
58
TT
»
57
P
* 42
12
86
49
36
79
54
"26
09
38
24
4l
86"
IT
79
G
< 08
28
67
68
66
94
22
63
71
66
83
IT
05
"of
58
H
* 95
60
19
62
"26
48
23
59
4o
38
15
67
43
92
42
J
62
77
43
79
54
69
38
65
16
82
10
96
67"
97
>
57
K
*“48
93
24
13
53~
29
46
37
32
65
12
94
84
95
”68
L
83
93
98
37~
75
79
ITS
1 2.
97
84
53”
03
75
76
95 *
M
* 31
29
32
21
"49
17
25
73
00
69
86
36
79
45
19
H
77
98
38
95
97
93
"94
98
72
42
59
00
08
50
44
P
27
26
62
57
06
91
23
;
RESTRICTED
4
REF ID : A56895
RESTRICTED
I
5* Solve the following cryptogram.
and
recover all keys:
80713
06941
35696
CVi
0
CO
1 3
2 8 0 6 1
3 7 6 9 5
69680
9 13 9 4
78800
255
1 3
28096
9 113 4
1* 7 7 1 3
6 8 0 2 6
97695
139
1 3
7 2 5 0 2
5 6 4 7 5
8 0 2 8 0
88091
3 5 8 0 2
252
4 7
3 13 4 1
39696
2 5 5 2 5
12508
09132
478
2 5
8 1 3 1 4
74256
6 9 5 2 5
5 13 0 1
36477
1
3 1
6 9
4 6 9 6 6
90699
8 0 2 4 7
46951
30801
8
0 5
2 5
113 7 8
0 4 4 7 0
6 9 2 1 3
113 0 8
03477
6. Solve the following cryptogram.
and
recover all keys:
18905
52131
89011
0
4 4
1 4
52131
3 4 0 2 2
0 5 5 1 8
9 2,0 2 2
3 5 15 6
1
9 0
0 5
5 2 2 4 0
5 5 14 5
1 9 0 2 0
2 15 6 1
67189
0
8 8
1 5
60110
4 4 19 0
0 8 8 0 1
119 0 0
22055
0
5 5
1 4
5 4 0 4 4
1 5 4 6 0
3 5 8 3 2
5 3 5 8 3
1 4 3 0 3
4
l 5
3 2
5 3 4 7 4
1 5 4 5 9
4 6 0 3 5
8 3 8 1 3
1 4 2 8 0
2
7 9 4 6
0 4 6 0 3
1 4 4 4 8
51628
0 3 14 3
5 8 4 0 4
3
3 6 3 7
0 4 0 4 4
1 5 2 9 1
3 7 0 3 1
43036
7 3 7 3 0
7
2 9 7 1
87296
7 3 6 8 4
7 0 7 5 7
26957
3 0 5 7 2
7
1872
9 7 0 7 5
7 2 5 5 0
5 7 2 6 1
7 6 8 4 7
29729
6
0 6 6 l
7 7 18 6
5 15 7 2
71871
85385
9 4 5 7 2
4
6
REF ID: A5 68 95
ttEOTmCTED
7* Solve' the following cryptogram, and recover all keys:
7 2 10 9
19015
4 17 7 6
04657
89925
9 6 2 3 5
7 0 3 6 8
62717
67091
8 3 9 3 8
9 9 2 9 4
88596
5 2 3 6 8
62170
3 7 0 9 1
22620
8 0 7 3 5
9 6 6 9 5
0 4 6-2 7
17032
- 5 3 l 3 6
7 7 6 4 4
2 2 5 3 7
1 2 2 6 2
47907
38026
* /
- 2 2 7 0 3
8 8 4 3 4
30196
0 4 118
6 6 8 2 6
2 7 0 3 4
1 5 5 9 6
8 4 8 2 5
3 5 2 3 0
46569
1 6 3 7 5
8 4 9 7 9
7 4 8 9 3
10920
85780
7 3 .5 4 1
9 7 4 7 7
67212
08479
3 5 2 1 0
9 13 6 5
78947
3 9 8 6 5
97030
2 8 3 3 4
1 5 4 3 2
54516
5 9 9 1 0
0 4 6 3 9
8 2 9 9 2
2 6 5 4 1
0 9 14 2
4 3 4 3 0
2 8 2 0 8
7 5 8 5 2
3 3 9 8 7
0 3 7 1 2
2 5 3 2 2
67217
5 8 5 7 8
RESTRICTED
7
REF ID : A56895
RESTRICTEB -
8. The following cryptograms are > suspected to he isologs* Solve
them, and recover all keys:
Message "A"
09728
2 3 14 4
3 3 9 8 7
7 3 5 1 4
2 7 7 6 9
IO677
9 4 4 l 8
9 9 4 7 9
4 19 4 8
6 6 4 3 2
2 4 3 7 4
4 8 4 9 9
5 6 7 5 8
4 7 6 3 6
3 5 5 4 6
81176
1 2 2 4 2
3 0 7 7 7
76194
1 5 2 7 2
6 2 6 4 4
8 5 2 1 1
2 13 6 1
71687
2 8 7 5 9
72459
47047
2 0 2 0 4
2 2 14 5
5 3 5 7 0
2 13 7 7
5 8 4 6 7
3 6 l 6 6
1 3,0 3 7
1
0 5 3 5 8
25876
6 4 4 0 3
3 3 5 2 4
3 6 8 4 7
9 8'
9 7 5
7 6 6 7 9
8 3 6 3 7
7 9 9 4 6
0 5 7 7 7
4 6 2 4 3
9 5
6 6 7
15086
4 7 9 2 0
5 4 3 9 1
2 7 2 8 4
32060
4 3i
17 8
9 4 3 6 7
6 6 4 1 4
32190
1 5 4 2 9
6 2 6 4 8
6 o' 9 7 5
4 7 9 1 5
6 6 6 7 9
1 4 4 2 2
70281
9 3 8 9 4
7 13 6 8
3 5 3 2 5
27686
2 17 0 7
79439
2 2 0 0 0
Message
"B"
8 7 5 6 0
7 7 4 4 4
3 5 2 1 1
4 110 9
I
3 3 7 7 2
8 9 0 8 4
5 5 4 1 5
78586
4 10 5 6
1
3 5; 5 0 6
1 5 8 4 4
48995
2 0 110
2 3 7 7 7
5 8 19 9
1 9',4 3 7
\
5 7 0 5 2
6 2 7 1 4-
37174
88756
2 5 15 4
1 1*7 2 4
9 8 7 7 9
72367
61813
38507
47890
6 8;7 1 9
6 5 5 2 l
08875
68548
81270
3 3 6 0 9
1
l 7'5 5 4
83811
7 2 4 7 7
85433
50805
3 7 5 9 8
6 0 ,7 1 8
3 7 3 0 6
1 7 7 0 4
06159
6 2 7 1 4
4 6 5 5 1
6 9
3 7 0
5 0 9 4 5
58696
1 9 5 6 1
70681
8 6 6 0 0
8 3
^•7 4
5 5 3 7 7
7 15 0 2
1 6 5 7 6
4 12 9 5
65052
0 0
7 5 1
1
47289
3 3 9 5 6
5 9 4 9 7
38764
6 6 5 7 4
72261
4
0 8 5 6 0
7 3 7 6 3
6 8 3 5 0
4 8 5 1 6
25000
•
RESTRICTED
8
REF ID: A5 68 95
RESTRICTED
9. The- following naval messages are suspected to "be isologs, con-
taining the probable word ‘'TASK FORCE” . Solve them, and recover all keys •
Message “A”
43022
8 3 5 2 4
2 6 0 6 0
9 8 4 4 8
5 6 17 5
5 7 3 6 8
05544
5 4 7 1 3
2 5 7 4 8
1 8 9 9 5
7 3 2 1 1
78809
78230
4 6 7 4 6
5 5 5 6 6
'38971"
5 2 8 3 5
5 4 3 1 0
66179
30225
49705
63605
7 5 3 1 0
8 3 4 5 2
92351
0 3 13 2
27998
9 3 5 3 9
26288
110 9 5
80473
1 2 2 0 0
6 3 3 6 9
4 £ 1 0 8
5 2 0 9 7
114 7 7
11306
6 8 7 2 1
98883
6 8 4 5 3
95650
15 18 4
59749
92076
67000
Message
77639
3 2 3 3 8
9 6 6 8 7
3 2 5 8 3
16771
3 6 0 3 3
25195
2 10 0 7
6 1 9 3 6
3 7 14 7
9 4 7 0 2
74323
91551
8 4 0 3 Q
2 3 2 1 1
74696
1 5 7 8 4
3 4 7 4 6
34170
5 9 3 9 1
3 5 5 8 4
1 7 6 4 5
6 5 7 5 2
24915
07432
6 4 5 9 8
9 9 10 4
1 7 3 0 7
6 6 6 3 9
3 112 7
9 0 4 0 2
5 3 3 5 3
77760
8 4 4 7 9
7 5 13 9
10388
0 2 2 8 5
4 2 2 1 4
8 0 13 2
6 2 5 6 8
1
2 7 5 2 9
4 2 8 7 5
07934
45455
2 0 0 0 0
RESTRICTED
REF ID: A5 68 95
RESTRICTED
10. The following cryptogram is suspected to begin with the opening
stereotype "REFERENCE YOUR MESSAGE....". Solve it, and recover all keys.
4 0 1 6 2
4 2 3 8 5
5 2 10 4
8 3 12 1
4 4 4 2 2
3 7 2 1 1
99099
4 2 12 7
3 7 9 1 2
7 7 7 8 5
80116
4 4 4 4 4
• 1 3 3 7 8
7 7 6 4 0
1 2 2 5 5
5 0 0 2 2
4 8 8 8 3
78850
22287
8 4 6 2 9
9 9 9 2 0
0 6 6 4 8
9 12 5 3
20729
0 13 3 1
81222
9.0 0 5 1
.9 9 5 2 3
1 9 3 9 1 •
41936
6 10 4 5
4 8 3 7 8
8 8 3 1 1
1 5 4 5 4
00022
05509
6 0 6 1 5
5 7 12 9
1 8 8 5 9
20396
6 6 6 0 3
14945
3 5 0 7 9
88552
8 2 4 1 1
0 8 6 6 3
05032
28600
0 7 7 2 2
5 5 2 1 2
0 0 0 8 0
0 0 7 7 4
72883
4 0 9 0 Q
RESTRICTED
§:
APPENDIX 2
TM FREQUENCY DATA - ENGLISH
REF ID : A56895
RESTRICTED
ENGLISH CRYPT ANALYTIC DATA
frequency tables
Table No. Pago
1-A. Absolute frequencies of letters appearing in five Sets of Governmental plain-text telegrams, each set
containing 10,000 letters, arranged alphabetically 4
1-B. Absolute frequencies of letters appearing in five sets of Governmental plain-text telegrams, each set
containing 10,000 letters, arranged according to frequency 5
1- C. Absolute frequencies of vowels, high-frequency consonants, medium-frequency consonants, and low-
frequency consonants appearing in five sets of Governmental plain-text telegrams, each set con-
taining 10,000 lGt)j6r8_.b..&_.akha.kBaUkaiii>.i.baBbaSfi>*St>S Kb.l.Bft.vB&a&ASt&aBaKSakBa.aaakM.* 6
2- A. Absolute frequencies of letters appearing in the combined five sets of messages totalling 60,000 letters, i
arranged alphabetically. = »=** 6
2-B. Absolute frequencies of letters appearing in the combined five sets of messages totalling 60,000 letters,
arranged according to frequency.. ***«**_.***._„*_. *. aa 6
2-0* Absolute frequencies of vowels, high-frequency consonants, medium-frequency consonants, and low-
frequency consonants appearing in the combined five sets of messaged totalling 60,000 letters.. *..* 6
2-D. Absolute frequencies of letters as initial letters of 10,000 words found in Governmental plain-text tele-
grams. (1) Arranged alphabetically and (2) arranged according to frequency...***.* * 6
2-E. Absolute frequencies of letters as final letters of 10,000 words found in Governmental plain-text tele-
grams. (1) Arranged alphabetically and (2) arranged according to frequency. ** 7
8. Relative frequencies of letters appearing in 1,000 letters based upon Table 2-B. (1) Arranged alpha-
betically, (2) arranged according to frequency, (3) vowels, (4) high-frequency consonants, (5) me-
dium-frequency consonants, and (6) low-frequency consonants .*..*„*. .*.*.*.**** 7-8
4. Frequency distribution for 10,000 letters of literary English, as compiled by Hitt. (1) Arranged
alphabetically and (2) arranged according to frequency... ..*»* * -*._*... 8
6. Frequency distribution for 10,000 letters of telegraphic English, as compiled by Sitt. (1) Arranged
alphabetically and (2) arranged according to frequency * . * . * . * , 8
G-A. Frequency distribution of digraphs, based on 50,000 letters of Governmental plain-text telegrams;
reduced to 6,000 digraphs....*... **.„._***...„..** ** 9
G-B. Frequency distribution of digraphs (naval text) based on 20,000 letters of naval text; reduced to
2,000 digraphs.-**-.**-...*..* *.** 10
7-11. Absolute frequencies of digraphs, trigraphs, and tetragraphs and the logarithms of their as-
signed probabilities * 11-88
7-A. The 428 different digraphs of Table 6-A, arranged according to their absolute frequencies, accom-
panied by the logarithms of their assigned probabilities..**** 18-16
7-B. The 18 digraphs composing 26% of the digraphs in Table 6-A, accompanied by the logarithms of
their assigned probabilities, arranged alphabetically according to their initial letters (1) and ac-
cording to their final letters (2) and according to their absolute frequencies * 16
7-C. The 63 digraphs composing 60% of the 5,000 digraphs in Table 6-A, accompanied by the logarithms
of their assigned probabilities, arranged alphabetically according to their initial letters (1) and ac-
^ cording to their final letters (2) and according to their absolute frequencies. 16
7-D. The 122 digraphs composing 76% of the 6,000 digraphs in Table 6-A, accompanied by the loga-
rithms of their assigned probabilities, arranged alphabetically according to their initial letters (1)
and according to their final letters (2) and according to their absolute frequencies 17-18
7-E. AU the 428 digraphs of Table 6-A, arranged first alphabetically according to their initial letters
and then alphabetically according to their final letters 18
8. The 428 different digraphs of Table 6-A, arranged first alphabetically according to their initial
letters and then according to their absolute frequencies under each initial letter, accompanied by
the logarithms of their assigned probabilities 19-21
9-A. The 428 different digraphs of Table 6-A, arranged first alphabetically according to their final
letters and then according to their absolute frequencies, accompanied by the logarithms of their
assigned probabilities 22-24
9-B. The 18 digraphs composing 26% of the 6,000 digraphs of Table 6-A, accompanied by the loga-
rithms of their assigned probabilities, arranged alphabetically according to their final letters (1) and
according to their initial letters (2) and according to their absolute frequencies 26
2-2
REF ID: A5 68 95
RESTRICTED
Table No. Page
9-C. The 53 digraphs composing 50% of the 5,000 digraphs of Table 6-A, accompanied by the loga-
rithms of their assigned probabilities, arranged alphabetically according to their final letters (1) and
according to their initial letters (2) and according to their absolute frequencies 26-26
9-D. The 122 digraphs composing 76% of the 6,000 digraphs of Table 6-A, accompanied by the loga-
rithms of their assigned probabilities, arranged alphabetically according to their final letters (1)
and according to their initial letters (2) and according to their absolute frequencies 26-28
9-E. All the 428 different digraphs of Table 6-A, arranged alphabetically first according to their final letters
and then according to their initial letters - 28
10-A. The 66 trigraphs appearing 100 or more times in the 60,000 letters of Governmental plain-text tele-
grams, arranged according to their absolute frequencies, accompanied by the logarithms of their
assigned probabilities — — - 28
10-B* The 66 trigraphs appearing 100 or more times in the 50,000 letters of Governmental plain-text tele-
grams, arranged first alphabetically according to their initial letters, and then according to their
absolute frequencies, accompanied by the logarithms of their assigned probabilities 29
10-C. The 66 trigraphs appearing 100 or more times in the 60,000 letters of Governmental plain-text tele-
grams, arranged first alphabetically according to their central letters, and then according to their
absolute frequencies, accompanied by the logarithms of their assigned probabilities 29-80
10- D. The 56 trigraphs appearing 100 or more times in the 60,000 letters of Governmental plain-text tele-
grams, arranged first alphabetically according to their final letters, and then according to their abso-
lute frequencies, accompanied by the logarithms of their assigned probabilities... 30
11- A. The 64 tetragraphs appearing 60 or more times in the 50,000 letters of Governmental plain-text
telegrams, arranged according to their absolute frequencies, accompanied by the logarithms of
their assigned probabilities— 31
11-B. The 54 tetragraphs appearing 60 or more times in the 50,000 letters of Governmental plain-text
telegrams, arranged first alphabetically according to their initial letters, and then according to their
absolute frequencies, accompanied by the logarithms of their assigned probabilities 81
11-C. The 54 tetragraphs appearing 60 or more times in the 50,000 letters of Governmental plain-text
telegrams, arranged first alphabetically according to their second letters, and then according to
their absolute frequencies, accompanied by the logarithms of their assigned probabilities. 82
11-D. The 64 tetragraphs appearing 60 or more times in the 60,000 letters of Governmental plain-text
telegrams, arranged first alphabetically according to their third letters, and then according to
their absolute frequencies, accompanied by the logarithms of their assigned probabilities ... 32-38
11-E. The 54 tetragraphs appearing 60 or more times in the 60,000 letters of Governmental plain-text
telegrams, arranged first alphabetically according to their final letters, and then according to their
absolute frequencies, accompanied by the logarithms of their assigned probabilities. ........ 83
12. Average length of words and messages. 84
13. Checkerboard individual frequencies - 86
14. Relative logarithmic values of frequencies of English digraphs 86
16* Relative logarithmic values (Logo 222) of frequencies of English digraphs 87
*****
SPECIAL-PURPOSE DATA
l6-A. Frequency distribution of digraphs, based on 64,3^5 letters of
decrypted U. S. Government messages in -which Z was used as a
word-separator and X was used for both Xp and Z..*,.. 38
l6-B. Frequency distribution of digraphs, based on the text used for
Table l6-A, from which the Z word-separator has been omitted
(total: 53,866 letters) ..... 39
l6-C • The 53 digraphs from Table 6-A which comprise 50$ of the to-
tal, arranged according to frequencies reduced to a base of
5,000 digraphs, shown with the corresponding frequencies of
the same digraphs from Table 16-B (also reduced to a base
of 5,000) 40
2-3
RESTRICTED
REF ID: A5 68 95
Tabus 1-A.-
each set containing 10,000 letters, arranged alphabetically
Absolute
Frequency
1,867
258
166
810
742
18
86
865
242
786
685
241
40
760
658
Absolute
Frequency
788
103
800
413
1,294
287
175
351
750
17
38
393
240
794
770
272
22
746
583
879
233
178
168
50
155
17
Absolute
Frequency
681
98
288
423
1,292
308
161
335
787
10
22
383
238
815
791
817
45
762
585
894
812
142
136
44
179
2
Absolute
Frequency
740
83
826
451
1,270
287
167
349
700
21
21
386
249
800
766
245
38
735
628
958
247
183
133
53
218
11
10,000
10,000
10,000
10,000
10,000
REF ID: A5 68 95
Table 1-B . — Absolute frequencies of letters appearing in five sets of Governmental plain-text telegrams,
each set containing 10,000 letters, arranged according to frequency
Table 1-C . — Absolute frequencies of vowels, high-frequency consonants, medium-frequency con-
sonants, and low-frequency consonants appearing in five sets of Governmental plain-text tele-
grams, each set containing 10,000 letters
Set No.
Vowels
High-Frequency
Consonants
Medium-Fre-
quency Conso-
nants
Low-Frequency
Consonants
3,993
3,527
2,829
151
3,985
3,414
2,457
144
4,042
3,479
2,356
'flBiiMiiMjM
3,926
8,672
2,358
144
3,942
8,646
2,389
123
Total 1
19,888
i
17,538
11,889
685
1 Grand total, 50,000,
2-6
REF ID: A5 68 95
RESTRICTED
Table 2-A. — Absolute frequencies of letters appearing in the combined five sets of messages totalling
. 50,000 letters, arranged alphabetically
A
3,683
G
819
L....
- 1,821
Q-
176
V,
766
B
..487
. H —
1,694
M
1,837
R--r*r-
3,788 .
ty
780
C.
1,634
I—
3,676
N
.. 3,976
S.
3,068
4,596
X
231
D
2,122
J..„.
82
0....
.. 3,764
T.
y
967
E.
P......
6,498
1,416
K
148
P....
.. 1,336
u...~
1,300
z
49
Table 2-B . — Absolute frequencies of letters appearing in Ike combined five sets of messages totalling
50,000 letters, arranged according to frequency
E
.... 6,498
I—
.... 3,676
C
.... 1,534
Y
967
X
.. 231
T.
.... 4,595
S
.... 3,058
F......
.... 1,416
G
819
Q
.. 175
N.
.... 3,975
D
.... 2,122
P
.... 1,335
W
780
K
.. 148
R....u
.._ 3,788
L
.... 1,821
U.
.... 1,300
V
766
J
82
0 ......
.... 3,764
H.
.... 1,694
M
.... 1,237
B
487
Z
.. , 49
A 3,683
Table 2-C . — Absolute frequencies of vowels, high-frequency consonants, medium-frequency con-
sonants, and low-frequency consonants appearing in the combined five sets of messages totalling
50,000 letters
Vowels — 19,888
High-frequency consonants (D, N, R, S, and T) 17,638
Medium-frequency consonants (B, C, P, G, H, L, M, P, V, and W) 11,889
Low-frequency consonants (J, K, Q, X, and Z) 686
Total - 50,000
Table 2-D . — Absolute frequencies of letters as initial letters of 10,000 words found in Governmental
plain-text telegrams
(1) ARRANGED ALPHABETICALLY
A
905
G„
109
L
.. 196
Q......
30
V
77
B
287
H..
272
M
.. 384
R......
.... 611
W
... 320
C
664
I_
344
N
.. 441
S.
.... 965
X
4
D
525
J..
44
0
.. 646
T......
.... 1,253
Y
88
E
390
K..
23
P
.. 433
U.
.... 122
Z
12
F
855
Total.
...10,000
(2) ARRANGED ACCORDING TO
FREQUENCY
T
1,253
R..
611
M
.. 384
L......
.... 196
J
44
S
965
D..
525
I
.. 344
U
.... 122
Q
30
A
905
N..
441
W.
.. 320
G.......
.... 109
K
23
F
855
P_.
433
B.
.. 287
Y
88
Z
12
C
664
E..
390
H
- 272
V
77
X
4
0
646
'
Total.
...10,000
REF ID: A5 68 95
RESTRICTED
Tablh 2-E . — Absolute frequencies of letters as final letters of 10,000 toords found in Governmental
plain-text telegrams
(1) ARRANGED ALPHABETICALLY
A
.... 269
G..
225
T.
354
Q
8
V
4
B
22
H„
450
M
154
R
769
W
45
C.
86
I_
'22
N ’
872
s...
962~
X.'.
... 116
D
.... 1,002
J..
6
0
575
T..'
1,007
Y
... 866
E
.... 1,628
K..
53
P
213
U..
31
Z....1...
9
F
.... 252
■
Total..
...10,000
(2) ARRANGED ACCORDING TO,
FREQUENCY
E
.... 1,628
R„
769
F
252
c_
86
I
22
T
.... 1,007
0 ..
575
G
225
K..
53
Z
9
D
.... 1,002
H„
450
P
213
W..
45
Q~ —
8
S
962
L..
354
M
154
u..
31
J
6
N.
.... 872
A..
269
X—
116
B..
22
V
4
Y......
.... 866
" _
‘
Total.... 10,000
Table 3. — Relative frequencies of letters appearing in 1,000 letters based upon Table 2-B
(1) ARRANGED ALPHABETICALLY
A
73.66
G™
16.38 L
36.42
Q
.3.50 V
.. 15.32
B
. 9.74
H„
33.88 M
24.74
R
75.76 W.
.. 15.60
a
30.68
I
73 . 52 N
"“79.50
s
61.16 Y
4.132
D
42.44
j....
1.64 0
-- 75.28
T
' 91.90 Y
„ 19. &4
E
129.96
K...,
2.96 P
..... 26.70
U.
‘26.00 Z
.68
F
.28.32
1
1,000.^0
Total....
(2) ARRANGED ACCORDING TO FREQUENCY
■■ 1
129.96
L.
73 . 52 C
SO.fiR
Y
19.34 Y
4.62
T
91.90
s...
’ 61.16 F
28.32
G
16.38 Q
.. 3.50
N
79.50
D...
42.44 P
26.70
W
15.60 K
_ 2.96
R
75.76
L...
36.42 IJ
26.00
V
1 5 . 32 .T
1.64
0
75.28
H...
33.88 M
24.74
B
9.74 Z
.98
A
73.66
Total
1,000.00
(3) VOWELS
(4) HIGH-FREQUENCY
A
73.66
CONSONANTS
E
• 129.96
D.
42.44
I
73.52
N
„
...... 79.50
o
75.28
R
75.76
U
26.00
s _
, ,
— 61.16
Y
19.34'
• T
__
...... 91, 90
Total 397.76
Total 350.76
REF ID: A5 68 95
DESTHIGTEB -
Tablb 8, Contd . — Relative frequencies of letters
(B) MEDIUM-FREQUENCY
CONSONANTS
B 9.74
C 30.68
F. 28.82
G 16.88
H........ ....... — .... ’88 ■ 88
f, 86.42
M 24.74
P 26.70
appearing in JiOOO letters based upon Table 2~B
•(6) LOW-FREQUjBNCY
CONSONANTS
X....... .......... ......... 4 . 62
$ 8.50
K 2.96
J 1.64
2 .98
Total 18.70
V 15.82
ff 15.60
Total (8), (4),
Total 237.78 ( 5 ), (6) 1,000.00
Table 4.—
-Frequency distribution for 10,000 letters of literary English, as
compiled by
•Hitt »
(1) ARRANGED ALPHABETICALLY
A.
778
G.
174 L
372 Q
8
V
112
B
141
H.
595 M
288 R
651
w
176
C
296
I.
667 N
686 S
622
X
27
D
402
J.
51 0
807 . T
856
Y ..
196
E
.. 1,277
K.
74 P
223 U
.308
Z
17
P
197
(2) ARRANGED ACCORDING TO FREQUENCY
E
.. 1,277
R_
651 n
308 Y
196
K
74
T
.. ' 855
s.
622 C
296 W
176
j
51
0
.. 807
H.
595 M
288 G
174
x
27
A
778
D.
402 P
223 B
141
z
17 '
N
_ 686
L.
372 F
197 V
112
Q
8
I
.. 667
Table 6.—
- Frequency distribution for 10,000 letters of telegraphic English, as compiled by Hitt 1 ■
(1) ARRANGED ALPHABETICALLY
A
... 813
G.
201 L
392 Q
38
V
136
B
... 149
H.
386 M
273 R
677
w
166
C
... 306
I,
711 N
718 S
656
X
51
D
._ 417
J.
42 0.... „
844 T
634
Y
208
E
1,319
K_
88 P_
243 U
321
Z
6
F
._ ' 205
(2) ARRANGED ACCORDING TO FREQUENCY
E
... 1,319
s.
. _.. 656 U
821 F
205
K .
88
0
... 844
T.
634 C
806 G
201
X_ _
51
A
... 813
D.
417 M
273 W
166
J
42
N
... 718
L.
- 392 P
243 B
149
Q
38
I
... 711
H.
386 Y
208 V
136
Z
6
R
... 677
i Hitt,
Capt. Parker.
Manual for the Solution of Military Ciphers. Army Service Schools Press, Fort 1
Leavenworth* Kansas* 1916.
res™
[OTEB-
2-8
REF ID: A5 68 95
Table 6-A. — Frequency distribution of digraphs, based on 50,000 letters of Governmental plain-text
telegrams; reduced to 5,000 digraphs
Second Letter
Total
ABC D E PGH IJKL M N 0 PQR S T UVWXYZ “T“ Blanks
alrj^li a> ■ ^ b "
REF ID: A5 68 95
REOTRICTED
Tables 7-11, Inclusive
Absolute frequencies of digraphs, trigraphs, and tetragraphs and the logarithms of their
assigned probabilities 1 t
1. For each of the following 18 tables, the basic data were first arranged according to their
absolute frequencies (F), and then the logarithms— L U (F) of the frequencies found.
2. The tables are designed to facilitate determination of the relative weights or probability
of occurrence of sets of digraphs, trigraphs, or tetragraphs, particularly with respect to various
“matching” operations. For example, are the matched digraphs BE and ET more probable than
the matched digraphs RT and EF? Table 7-A shows the frequencies (F) of the digraphs to be
as follows: RE =98, ET=S7, RT=42, EF=18. Therefore, 98 times 87 is compared with 42
times 18, or 8,626 with 756. This arithmetic method of approach is extremely cumbersome for
a large number of comparisons. By using the logarithms of the individual frequencies, the opera-
tion is greatly simplified, since the addition of the logarithms of two numbers is equivalent to
the multiplication of their equivalent arithmetic values. Thus, the foregoing computation may
be expressed as Log 98+Log 37, compared with Log 42-4-Log 18, or 0.96+0.79 versus 0.81+0.66
(see Table 7-A and explanation below). If more than one occurrence of a particular digraph is
involved, it is merely necessary to multiply the logarithmic value by the number of the occur-
rences, viz., Log X+2(Log Y)+3(Log Z), as compared with Log A+3(Log B)+2(Log G).
3. The logarithm of any given number is the power to which 10 must be raised to equal the
given number. Thus, 10 2 =100, or the logarithm of 100=2. Similarly, 10* =1,000, or the loga-
rithm of 1,000 = 3. The sum of logarithms is equal to the logarithm of the product of their antilogs
(arithmetic numbers they represent). For example, 10 2 =100; 10*=1000; 10* +, =100X1000; Log
100,000 = 5. Also, 10° = 1, or Log 1=0. The Log of 0 is minus infinity (- 00 ).
4. In the compilation of the logarithms of the elements constituting these tables, frequencies
of 1, of course, had a logarithmic value of 0.00. Digraphs which did not occur,* i.e., those with
0 occurrences, had a logarithmic value of minus infinity (-<*>). For practical use, each of
the original frequency occurrences in these tables was doubled; i. e., EN was given a frequency
of 222 instead of 111, the frequency of RE became 196 instead of 98, etc. Thus, single occur-
rences were doubled (2X1=2), and the logarithms of those elements became 0.30 instead of 0.
This is equivalent to saying Log 1+Log 2=0.00+0.30=0.30. Those elements which occurred
0 times, now were assumed to have ah occurrence of 1, with an equivalent logarithmic value of 0.00.
5. In order to place all the logarithms of the initial frequencies on a comparable logarithmic
basis, it was merely necessary to add 0.30 to each of them. While EN had a frequency of 111
in the original compilation, it now had a frequency of 222, or 2(111). The logarithm of 222 is
2.35. This is equivalent to saying Log 111+ Log 2=2.06+0.30=2.35.
6. The frequencies as stated in terms of their actual logarithms do not readily indicate their
relative size for each distribution. Therefore, the highest frequency in each group was given a
value of 0.99, and the lowest a value of 0; frequencies intermediate between these extremes were
i These frequency distributions are based upon data derived from 60,000 letters of U. 8. Governmental plain-text telegrams, reduced to 6,000
digraphs.
9 While in general it is possible to assign probability values to digraphs in accordance with their observed frequencies, it Is not Btrictly correct
to associate the probability “0" with a frequency of zero. This would be equivalent to saying: "Because a specified digraph has not occurred, it
cannot occur,” and would be reflected in the mathematics: "log probability zero equals minus infinity.” What may be said is: "Since a spoclfiod
digraph has not occurred in the data its true probability value is unknown, except that it must be below the probability value assigned to a fre-
quency of one.” The proper way to assign a probability value to digraphs with frequencies of zero Is to continue counting until they have at
least one occurrence; then the true relative probability can bo found.
A simple practical method of taking this difficulty into account is merely to assume that in twice the amount of data the digraph probably
would have occurred at least once; that Is, it has a frequency of one-half.
It should be pointed out, however, that since probabilities are multiplied (by summing logarithms) a 10% error in evaluating the digraph ZZ
for example, makes tho product, wherever ZZ occurs, 10% wrong, and is just as serious os a 10% error in evaluating the high-frequency digraph EN.
In practice, however, results obtained from the logarithmic method are so satisfactory that refinements are not needed.
2-11
REOTRICTED
REF ID: A5 68 95
RESTRICTED
evaluated in proportion to their respective frequencies! 'fliia is equivalent to expressing the
frequencies in logarithms with a base ot|ier than 10 . In other words, flits' procedure of don Voting'
the logarithms to the rangte from .00 to .09 consists in dividing up the original Yange of logarithms-
into 100 equal parts and assigning each one to the proper rank in the rang®’.
7. The new base (C) used to convert each of the djgraphic frequencies to the logarithmic
range 0 to 0.90 is derived as follows, when 222 is the highest frequency (F):-
Lel‘228=C # - 9tf
IiOgio 222=Logio C ° 00
Logio 222 = (0.99) (Log 10 C)
„ A , Logi 0 222 A x „- 2.35
O = Anlilog -^ 99 - = Antilog Q ^
C =224
8 . The formula for the computation of the logarithm to the new base (C) of any actual
frequency (Y) of a series isi
Log 0 Y =
Login Y
Logm (J
II is more expeditious to use reciprocals in the conversion of a whole series of logarithmic values,
ns in this instance. The formula is: (Logm C)" 1 . (Log lQ Y) =Log 0 Y.
9. The digraphic index chart, Table 16, on page 37, summarizes the logarithmic frequencies
of all English plain-iexl digraphs, computed to a base of 224. so that the logarithm of the highest
frequency (EN) is 0.99.
Example : EN «= 222
Log io 222 = 2.35
(Logio C ) _1 = (Logi 0 224)" 1 =0.421
Log. 222 =0.421 X2.35 =0.99
10* Likewise, the trigraphs and tetragraphs have been, computed to the
bases L 586 and. Lehk, respectively, so that the logarithms of the highest-
frequency trigraph (EHT) and tetragraph (TION) are 0*99* Since no use is
being made of the trigraphs appearing less than 100 times and tetragraphs
appearing less than 50 times, the basic frequencies of the trigraphs and
tetragraphs have not been doubled in computing the new bases of the loga-
rithms.
2-12
RESTRICTED
REF ID : A56895
RESTRICTED
Table 7-A . — The 428 different digraphs of Table 6-A, arranged according to their absolute frequencies,
accompanied by the logarithms of their assigned probabilities
p
Lm(F)
Ij224
(2F)
P
Lio(F)
rnLum
HHHI
Lio(F)
msm
P
Ljo(F)
JjH 4
<2F)
EN
Lll
2.05
.99
DA....
32
1.51
.76
ES
1.28
.67
EQ-.
12
1.08
.68
RE
98
1.99
.96
EC....
32
1.51
.76
m
1.28
.67
0D —
12
1.08
.68
ER
87
1.94
.94
RS..__
31
1.49
.75
ss..__
19
1.28
.67
SF
12
1.08
.58
NT....
82
1.91
.93
UR
31
1.49
.75
TS._._
19
1.28
.67
US....
12
1.08
.58
TH....
78
1.89
.92
NI
30
1.48
.75
TT..._
19
1.28
.67
UT....
12
1.08
.58
ON....
77
1.89
.92
RI
30
1.48
.75
WO....
19
1.28
.67
VI....
12
1.08
.58
IN
75
1.88
.92
EL....
29
1.46
.74
BE
18
1.26
.66
WA._..
12
1.08
.58
TE
71
1.85
.91
HT
28
1.45
.74
EF
18
1.26
.66
FF.._.
11
1.04
.56
AN....
64
1.81
.89
LA....
28
1.45
.74
NO....
18
1.26
.66
FT....
11
1.04
.56
OR
64
1.81
.89
RO....
28
1.45
.74
PR....
18
1.26
.66
PP.._
11
1.04
.56
ST....
63
1.80
.88
TA.._.
28
1.45
.74
AI
17
1.23
.64
RR....
11
1.04
.56
ED....
60
1.78
.88
*2.495
HR....
17
1.23
. 64
SU....
11
1.04
.56
NE_._.
57
1.76
.87
PO....
17
1.23
. 64
UE_...
11
1.04
.56
VE.„.
57
1.76
.87
AD....
27
1.43
.73
RD
17
1.23
.64
YF
11
1.04
.56
ES
54
1.73
.86
DI__
27
1.43
.73
TR..._
17
1.23
,.64
YS
11
1.04
. 56
ND_...
52
1.72
.85
El....
27
1.43
.73
DO....
16
1.20
.63
FE
10
•
.55
TO....
50
1.70
.84
IR....
27
1.43
.73
DT
15
1.18
.62
IF....
10
!
.55
SE
49
1.69
.84
IT....
27
1.43
.73
IX....
15
1.18
.62
LY....
10
.55
*1.249
LL....
27
1.43
.73
QU_...
15
1.18
.62
M0....
10
IK 1
.55
NG....
27
1.43
.73
SO....
16
1.18
.62
SP....
10
[If' ;
.55
AT....
47
1.67
.83
ME,
26
1.41
.72
YT.__.
15
1.18
.62
Y0_...
10
If |
.55
TI
45
1.65
.82
NA_._.
26
1.41
.72
AC....
14
1.15
.61
FR
9
.53
AR....
44
1.64
.82
SH
26
1.41
.72
AM....
14
1.15
.61
IM....
9
flf r
.53
EE....
42
1.62
.81
IV_._
25
1.40
.72
CH_...
14
1.15
.61
LD._..
9
0.95
.53
RT....
42
1.62
.81
OF....
25
1.40
.72
CT....
14
1.15
.61
MI....
9
0.95
.53
AS
41
.80
0M..._
25
1.40
.72
EM
14
1.15
.61
NF
9
0.95
.53
CO....
41
1.61
.80
OP....
25
1.40
.72
GE
14
1.15
.61
RC
9
0.95
.53
10....
41
1.61
.80
NS....
24
1.38
.71
OS
14
1.15
.61
RM
9
0.95
.53
TY
41
1.61
.80
SA....
24
1.38
.71
PA....
14
1.16
.61
RY
9
0.95
.53
FO
40
.80
IL____
23
1.36
.70
AU..._
13
1.11
.59
YE
9
0.96
.53
FI
39
1.59
.80
PE
23
1.36
.70
DS....
13
1.11
.59
DD
8
0.90
.61
RA
39
1.59
.80
IC_...
22
1.34
.69
IE
13
1.11
.59
DF....
8
0.90
.51
ET
37
1.57
.79
WE....
22
1.34
.69
LO
13
1.11
.59
HU....
8
0.90
.51
LE~.„
37
.79
UN....
21
1.32
.68
MM
13
1.11
.59
IA
8
0.90
.51
OU....
37
1.57
.79
CA..__
20
1.30
.67
PL....
18
1.11
.59
LT
8
0.90
.51
MA....
36
1.56
.78
EP.._.
20
1.30
.67
RP-.
13
1.11
.69
MP
8
0.90
.61
TW....
36
1.66
.78
EV—
20
1.30
.67
SC....
13'
1.11
.59
NN_._.
8
0.90
.51
EA....
35
1.64
.78
GH-.
20
1.30
.67
WI..__
13!
1.11;
.59
OC_...
8
0.90
.51
IS....
35
1.54
.78
HA._._
20
1.30
.67
*3.745
0W_...
8
0.90
.51
SI....
34
.77
HE....
20
1.30
.67
PT__._
8
0.90
.51
DE
33
1.52
.77
HO....
20
1.30
.67 '
AP....
12
1.08
.68
UG....
8
0.90
.51
HI....
33
1.52
.77
LI....
20
1.30
.67
AY....
12
1.08
.58
AV
7
0.85
.48
AL-.
32
1.51
.76
IG....
19
1.28
.67
DR....
12
1.08
.58
BY
7
0.85
.48
CE
32
1.51
.76
NC-.
19
1.28
.67
E0..._
12
1.08
.58
Cl
7
0.85
.48
* Tho IS digraphs above this lino compose of tl.o total. * The 122 digraphs above this JIne compose 75% of the total,
s Thu 63 digraphs above this line compose 60% of Ihu total.
2-13
R ESTRICTED
\
REF ID: A56895
RESTRICTED
Table 7-A, Contd . — The 428 different digraphs of Table 8-A, arranged according to their
absolute frequencies, accompanied by the logarithms of their assigned probabilities
F
L»(F)
Lit*
<2F>
F
L»(F)
F
£-»(F)
F
Iiio(F)
0}
EH
7
.48
RU.™
5
0.70
.42
GS
3
0.48
.33.
JE™.
2
m
.25
EW
7
0.85
.48
RV™.
5
0.70
.42
HC.™
3
0.48
.33
JO™.
2
m
.25
EX
7
0.85
.48
SD
5
0.70
.42
HN
3
0.48
.33
JU.™
2
EE
.25
GA
7
0.85
.48
SR.™
5
0.70
.42
LB
3
0.48
.33
KI
2
m
.25
IP..„
7
0.85
.48
TL
5
0.70
.42
LC
3
0.48
.33
LM.™
2
.25
NU.„.
7
0.85
.48
TU
5
0.70
.42
LF
3
0.48
.33
LR.™
2
si
.25
OA.™
7
0.86
.48
UA
5
0.70
.42
LP.™
3
0.48
.33
LU.™
2
.25
OV.™
7
0.85
.48
UI.™
5
0.70
.42
MC
3
0.48
.33
LV™.
2
m
.25
RG.„.
7
0.85
.48
UM
5
0.70
.42
NP
3
0.48
.33
LW.™
2
0.30
.25
RN™.
7
0.85
.48
AF
4
0.60
.38
NV.™ ,
3
0.48
.33
MR.
2
.25
TF™.
7
0.85
.48 •
BA
4
0.60
.38
NW '
3
0.48
.33
MT.™
2
0.30
.25
TN™.
7
0.85
.48
BO
4
0.60
.38
OE.™
3
0.48
.33
MU™.
2
EE
.25
XT.™
7
0.85
.48
CK..„
4
0.60
.38
OH
3
0.48
.33
MY.™
2
m
.25
AB.™
6
0.78
.45
CR.™
4
0.60
.38
PH
3
0.48
.33
NB
2
.25
AG„„
6
0.78
.45
CU„_
4
0.60
.38
PU™.
3
0.48
.33
NK„_
2
0.30
.25
BL.._
6
0.78
.45
DB
4
0.60
.38
RH
3
0.48
.33
OG.™
2
.25
GO™.
e
0.78
.45
DC.„
4
0:60
.38
SB....
3
0.48
.33
OK....
2
0.30
.25
ID....
6
0.78
.45
DN
4
0.60
.38
SM
3
0.48
.33
OY.™
2
EE
.25
KE„.
6
0.78
.45
DW.™
4
0.60
.38
TB
3
0.48
.33
PF.™
2
m
.25
LS™.
6
0.78
.45
EB_...
4
0.60
.38
UB....
3
0.48
.33
RB
2
8$
.25
MB™.
6
0.78
.45
EG....
4
0.60
.38
UC.™
3
0.48
.33
SG.™
2
m
.25
00....
6
0.78
.45
EY
4
0.60
.38
UD
3
0.48
.33
SL
2
0.'30
.25
PI.™
6
0.78
.45
GT
4
0.60
.38
YI
3
0.48
.33
TP.™
2
0.30
.25
PS.™
6
0.78
.45
HS.™
4
0.60
.38
YP.._
3
0.48
.33
UP.„
2
0.30
.25
RF.™
6
0.78
.45
MS._
4
0.60
.38
AH....
2
0.30
.25
WN™.
2
0.30
.25
TC.™
6
0.78
.45
NH
4
0.60
.38
AK
2
0.30
.25
XA.™
2
0.30
.25
TD
6
0.78
.45
NR
4
0.60
.38
AO
2
0.30
.25
xc.™
2
.25
TM
6
0.78
.45
OB
4
0.60
.38
BI
2
0.30
.25
XI....
2
0.30
.25
UL
6
0.78
.45
PM
4
0.60
.38
BR.™
2
0.30
.25
XP.™
2
.25
VA....
6
0.78
.45
RW
4
0.60
.38
BU.™
2
0.30
.25
YB.™
2
0.30
.25
YA.™
6
0.78
. 45
SN —
4
0.60
.38
DG.™
2
0.30
.25
YL.™
2
.25
YN.™
6
0.78
.45
S W.™
4
0.60
.38
DH.™
2
0.30
.25
YM.™
2
0.30
.25
CL....
5
0.70
.42
WH„.
4
0.60
.38
DQ.™
2
0.30
.25
ZE.™
2
0.30
.25
DM....
5
0.70
.42
YC.™
4
0.60
.38
FC.™
2
0.30
.25
AE.™
1
.13
DP.™
6
0.70
.42
YD.™
4
0.60
.38
FL.™
2
0.30
.25
AJ
1
.13
DU.™
5
0.70
.42
YR.._
4
0.60
.38
GC....
2
0.30
.25
BJ
1
.13
FA....
5
0.70
.42
AA....
8
0.48
.33
GF....
2
0.30
.25
BM.™
ll
.13
GI.™
5
0.70
.42
AW.™
3
0.48
.33
GL....
2
0.30
.25
BS.™
1
.13
GR....
5
0.70
.42
CC.™
3
0.48
.33
GP.™
2
0.30
.25
BT.___
1
.13
HF
5
0.70
.42
DL
3
0.48
.33
GU
2
0.30
.25
CD....
1
.13
NL
5
0.70
.42
. DV
3
0.48
.33
HD —
2
0.30
.25
CF_...
1
.13
NM
5
0.70
.42
EU
3
0.48
.33
HM
2
0.30
.25
CM....
1
.13
NY....
5
0.70
.42
FS
3
0.48
.33
IB....
2
0.30
.25
CN.™
1
.13
01 .™
5
0.70
.42
FU....
3
0.48
.33
IK....
2
0.30
.25
CS.™
1
.13
RL ..
5
0.70
.42
GN.__.
3
0.4S
.33
IZ.__.
2
0.30
.25
cw.™
1
.13
2-14
RESTRICTED
REF ID: A5 68 95
Table 7-A, Concluded. — The 428 different digraphs of Table 6-A, arranged according to their
absolute frequencies, accompanied by the logarithms of their assigned probabilities
F
L«(F)
Irtlt
(2F)
F
Lio(F)
(2F)
F
IMF)
■Pf
Kh
F
Lio(F)
Liu
<2F)
CY
1
0.00
.IS
HW—
1
0.00
.13
PD
1
0.00
.13
B
0.00
.13
DJ..„
1
0.00
.13
HY
1
0.00
.18
PN—
1
0.00
.13
m
0.00
.13
DY
1
0.00
.13
JA
1
0.00
.18
PV
1
0.00
.13
ws..„
i
0.00
.18
EJ
1
0.00
.13
KA
1
0.00
.13
PW
1
0.00
.13
WY—
i
0.00
.13
EZ
1
0.00
.18
KC
1
0.00
.13
PY—
1
0.00
.13
XD
i
0.00
.13
FD
1
0.00
.13
KL
1
0.00
.13
QM —
1
0.00
.13
XE
i
0.00
.13
FG
1
0.00
.13
KN
1
0.00
.13
QR
1
0.00
.13
XF....
i
0.00
.13
FM
1
0.00
.13
KS
1
0.00
.18
RJ
1
0.00
.13
XH—
i
0.00
.13
FP
1
0.00
.13
LG
1
0.00
.13
RK.„..
1
0.00
.13
XN —
i
0.00
.13
FW
1
0.00
.13
LH
1
0.00
.13
SK —
1
0.00
.13
XO—
i
0.00
.13
FY
1
0.00
.13
LN
1
0.00
.13
SV—
1
0.00
.13
XR—
i
0.00
.13
GD
1
0.00
.13
MD
1
0.00
.13
SY
1
0.00
.13
XS—
i
0.00
.13
GG
1
0.00
.13
MF
1
0.00
.13
TG
1
0.00
.13
YG
i
0.00
.13
GJ
1
0.00
.13
MH
1
0.00
• 1?
TQ
1
0.00
.13
YH
i
0.00
.13
GM
1
0.00
.13
NJ
1
0.00
.13
TZ
1
0.00
.13
YU
i
0.00
.13
GW
1
0.00
.13
NQ
1
0.00
.13
UF
1
0.00
.13
YW—
i
0.00
.13
HB
1
0.00
.13
OiI-
1
0.00
.13
UO
1
0.00
.13
ZA
i
0.00
.13
HL
1
0.00
.13
OX—
1
0.00
.13
UV
1
0.00
.13
ZI
i
0.00
.13
HP
1
0.00
.13
PB—
1
0.00
.13
VO
1
0.00
.13 J
5.000
HQ
1
O.OOl
.13
PC....
1
0.00
.13
VT
1
0.00
.13 ,
Table 7-B. — The 18 digraphs composing 25% of the digraphs in Table 6-A, accompanied by the
logarithms of their assigned probabilities, arranged alphabetically according to their initial letters
(1) AND ACCORDING TO THEIR FINAL (2) AND ACCORDING TO THEIR ABSOLUTE
LETTERS FREQUENCIES
F
IMF)
■H
F
LioCF)
mmm
F
IMF)
wm.
F
IMF)
mmm
AN....
64
1.81
.89
ON....
77
1.89
.92
AN..
.. 64
1.81
.89
ON....
77
1.89
.92
OR....
64
1.81
.89
OR....
64
1.81
.89
ED....
60
1.78
.88
RE....
98
1.99
.96
EN..
..111
2.05
.99
RE....
98
1.99
.96
EN....
111
2.05
.99
ER..
.. 87
1.94
.94
ER
87
1.94
.94
SE
49
1.69
.84
ED..
.. 60
1.78
.88
ST....
63
1.80
.88
ES
54
1.73
.86
ST
63
1.80
.88
ES..
.. 54
1.73
.86
SE—
49
1.69
.84
TE....
71
1.85
.91
i
TO-
78
1.89
.92
IN....
75
1.88
.92
TH....
78
1.89
.92
IN-
.. 75
1.88
.92
TE....
71
1.85
.91
i
1
TO—
50
1.70
.84
TO—
50
1.70
.84
ND._„
52
1.72
.85
VE.._.
57
1.76
.87
NT..
... 82
1.91
.93
VE—
57
1.76
.87
NE.___
57
1.76
.87
1,
249
NE..
... 57
1.76
.87
1,
249
NT....
82
1.91
.93
r
ND„
_ 52
Ena
.85
2-15
- REQTRICTED "
REF ID: A5 68 95
Table 7-C. — The 58 digraphs composing 50% of the 5,000 digraphs of Table 6-A, accompanied by
the logarithms of their assigned probabilities, arranged alphabetically according to their initial letters
(1) AND ACCORDING TO THEIR PINAL (2) AND ACCORDING TO THEIR ABSOLUTE
LETTERS FREQUENCIES
F
Lio(F)
B9
. F
Lio(F)
I.9M
<2F)
F
Lu(F)
■H
F
Lio(F)
Xitti
(2F)
AL
32
1.51
.76
MA
36
1.66
.78
AN....
64
1.81
.89
MA....
36
1.66
.78
AN
64
1.81
.89
AT....
47
1.67
.83
AR
44
1.64
.82
ND
52
1.72
.85
AR....
44
1.64
.82
NT....
82
1.91
.93
AS....
41
1.61
.80
NE
57
1.76
.87
AS....
41
1.61
.80
NE—
57
1.76
.87
AT....
47
1.67
.83
NI
30
1.48
.75
AL....
32
1.51
.76
ND....
52
1.72
.85
NT
82
1.91
.93
NI—
30
1.48
.75
CE
32
1.51
.76
CO....
41
1.61
.80
CO....
41
1.61
.80
ON....
77
1.89
.92
CE....
32
1.51
.76
ON—
77
1.89
.92
OR....
64
1.81
.89
OR—
64
1.81
.89
DA_..
32
1.51
.76
OU—
37
1.57
.79
DE.._
33
1.52
.77
OU—
37
1.57
.79
DE....
33
1.62
.77
DA....
32
1.51
.76
RA—
39
1.59
.80
RE....
98
1.99
.96
EA—
35
1.54
.78
RE....
98
1.99
.96
EN....
111
2.05
.99
RT....
42
1.62
.81
EC....
32
1.51
.76
RI—
30
1.48
.75
ER....
87
1.94
.94
RA....
39
1.59
.80
ED....
60
1.78
.88
RO—
28
1.46
.74
ED....
60
1.78
.88
RS—
31
1.49
.75
EE....
42
1.62
.81
RS
31
1.49
.75
ES....
54
1.73
.86
RI—
30
1.48
.76
EL....
29
1.46
.74
RT
42
1.62
.81
EE....
42
1.62
.81
RO—
28
1.45
.74
EN 111
2.05
.99
ET
37
1.57
.79
ER....
87
1.94
.94
SE—
49
1.69
.84
EA
35
1.54
.78
ST—
63
1.80
.88
ES.._.
54
1.73
.86
SI....
34
1.53
.77
EC
32
1.51
.76
SE—
49
1.69
.84
ET
37
1.67
.79
ST....
63
1.80
.88
EL—
29
1.46
.74
SI—
34
1.53
.77
FI
39
1.59
.80
TA-
28
1.45
.74
FO
40
1.60
.80
TO-
78
1.89
.92
FO
40
1.60
.80
TE—
71
1.85
.91
FI
39
1.69
.80
TE—
71
1.85
.91
TH—
78
1.89
.92
TO—
50
1.70
.84
HI—
33
1.52
.77
TI-
45
1.65
.82
HI
33
1.52
.77
TI—
45
1.65
.82
HT—
28
1.45
.74
TO—
50
1.70
.84
HT
28
1.45
.74
TY....
41
1.61
.80
Tff
36
1.56
.78
TW—
36
1.66
.78
IN....
75
1.88
.92
TY
41
1.61
.80
IN
75
1.88
.92
TA—
28
1.45
.74
10....
41
1.61
.80
10
41
1.61
.80
IS—
35
1.64
.78
UR
31
1.49
.75
IS-
35
1.54
.78
UR—
31
1.49
.75
LA....
28
1.45
.74
VE
57
1.76
.87
LE-
37
1.57
.79
VE—
57
1.76
.87
LE....
37
1.57
.79
2,495
LA....
28
1.45
.74
2,495
t
16
REF ID: A56895
nEOTfllCTED
Table 7-D . — The 122 digraphs composing 75% of the 5,000 digraphs of Table 6-A, accompanied
by the logarithms of their assigned probabilities, arranged alphabetically according to their
initial letters
* ■ , . T
(1) AND ACCORDING TO THEIR FINAL LETTERS
F
L»(P)
F
rwF)
■qi
■33S
F
L»(F)
■fy
Kill
F
Lw(F)
MEM
ESI
AC
14
1.15
.61
ER™
87
1.94
.94
MA...
36
1.56
.78
RS™.
31
1.49
.75
AD
27
1.43
.73
ES™
54
1.73
.86
ME...
26
1.41
.72
RT
42
1.62
.81
AX
17
1.23
.64
ET.„
37
1.57
.79
AL
32
1.51
.76
EV_.
20
.67
NA...
26
1.41
.72
SA
24
1.38
.71
AM
14
1.15
.61
NC...
19
1.28
.67
SE
49
1.69
.84
AN....
64
1.81
.89
FI_
39
1.59
.80
ND...
52
1.72
.85
SH
26
1.41
.72
AR
44
1.64
.82
FO™
40
1.60
.80
NE.__
57
1.76
.87
SI™.
34
1.53
.77
AS....
41
1.61
.80
NG...
27
1.43
.73
SO™.
15
1.18
.62
AT....
47
1.67
.83
GE™
14
1.15
.61
NI...
30
1.48
.75
ss....
19
1.28
.67
AU-...
13
1.11
.59
GH„.
20
1.30
.67
NO...
18
1.26
.66
ST....
63
1.80
.88
BE
18
1.26
.66
NS...
24
1.38
.71
HA...
20
1.30
.67
NT...
82
1.91
.93
TA.™
28
1.45
.74
CA
20
1 20
07
HE...
20
1.30
.67
TE™.
71
1.85
.91
ft?
22
JL* WV
i VI
70
HI...
33
1.52
.77
OF...
25
1.40
.72
TH_..
78
1.89
.92
wCi
flu
o&
1 A
JL • 01
• iO
01
HO...
20
1.30
.67
OL...
19
1.28
.67
TI™.
45
1.65
.82
un — _
no
41
1* J.U
20
HR...
17
1.23
.64
OM...
25
1.40
.72
TO....
50
1.70
.84
wU....
CT
fr JL
14
A • UA
1 1 R
• ou
01
HT...
28
1.45
.74
ON...
77
1.89
.92
TR.™
17
1.23
.64
A • AU
. UA
OP...
25
1.40
.72
TS.._
19
1.28
.67
DA....
32
1.51
.76
IC...
. 22
1.34
.69
OR...
. 64
1.81
.89
TT..._
19
1.28
.67
DE
33
1.52
.77
IE...
. 13
1.11
.59
OS...
. 14
1.15
.61
TW
36
1.56
.78
DI
27
1.43
.73
IG...
. 19
1.28
.67
OT...
. 19
1.28
.67
TY™.
41
1.61
.80
DO
16
1.20
.63
IL...
. 23
1.36
.70
OU...
. 37
1.57
.79
DS
13
1.11
1 .59
IN...
. 75
1.88
.92
UN-
21
1.32
.68.
DT
15
1.18
.62
10 ...
. 41
1.61
.80
PA...
. 14
1.15
.61
UR....
31
1.49
.75
IR...
. 27
1.43
.73
PE...
. 23
1.36
.70
EA
35
1.64
.78
IS...
. 35
1.64
.78
PO...
. 17
1.23
.64
VE™.
57
1.76
.87
EC
32
1.51
.76
IT...
. 27
1.43
.73
PR...
. 18
1.26
.66
ED
60
1.78
.88
IV...
. 25
1.40
.72 ’
WE....
22
1.34
.69
EE
42
1.62
.81
IX...
. 15
1.18
.62
QU...
. 15
1.18
.62
W0„.
19
1.28
.67
EF
18
1.26
.66
El
27
1.43
.73
LA...
. 28
1.45
.74
RA...
. 39
1.59
.80
YT.i.~
15
1.18
.62
EL
29
1.46
.74
LE...
. 37
1.57
.79
RD...
. 17
1.23
.64
3,'
745
EM....
14
1.15
. 61
LI...
. 20
1.30
.67
RE...
. 98
1.99;
.96
EN 111
2.05
.99
LL...
. 27
1.43
.73
RI„
. 30
1.48
.75
EP—
20
1.30
.67
LO...
. 13
1.11
.59
RO.,.
. 28
1.45
.74
,
1
REF ID: A5 68 95
Ull.kiJ.UlU 1JUU
Table 7-D, Concluded . — The 122 digraphs composing 75% of the 5,000 digraphs of Table 6-A,
accompanied by the logarithms of their assigned probabilities, arranged alphabetically according
to their initial letters
(2) AND ACCORDING TO THEIR ABSOLUTE FREQUENCIES
Table 7- E . — All the 128 digraphs of Table 6-A, arranged first alphabetically according to their
initial letters and then alphabetically according to their final letters .
(SEE TABLE 6-A.— READ ACROSS THE ROWS)
2 - 18
REF ID: A56895
RESTRICTED
Table 8. — The 1$8 different digraphs of Table 6-A, arranged first alphabetically according to their
initial letters and then according to their absolute frequencies under each initial letter, 1 accompanied
by the logarithms of their assigned probabilities
1 For arrangement alphabetically first under initial letters and then under final letters, see Table 6-A.
2-19
RESTRICTED
REF ID: A56895
HHTrJ.MW
Tadlb 8, Contd . — The J$8 different digraphs of Tails <S-A, arranged first alphabetically according
to their initial letters and then according to t heir absolute frequencies under each initial letter, 1
accompanied by tlte logarithms of their assigned probabilities
2-2Q
~ REO TRIG TED
REF^
A5 68 95
‘ \
V
Tablh 8, Concluded . — The 128 different difraqlis of Table 6-A, arranged first alphdbeticaMy accord-
ing to their initial letters and then according to their absolute frequencies under each initial letter, 1
• _ 1 T. if 1 *»T « • • • ■» 7.
F
Lia(F)
Liu
(ZF)
F
| Ljb(F)
f'Tfr-i
(2F) |
F
WF)
■^1
F
140(F)
tmm
RE
98
1.99
19
SR....
5
HBH
m
US—
12
HB!
.58
XI—
2
0.30
.25
RT
42
1.62
SN.._
4
MBit]
IBal
UT—
12
.58
XP—
2
0.30
.25
RA
39
1.59
EH
SW
4
mm
UE
11
HQ
.56
XD—
1
0.00
.13
RS
31
1.49
.75
SB
3
0.48
.33
UG
8
HR?
.51
XE
1
0.00
.13
RI
30
1.48
.75
SM.
3
0.48
.33
UL
6
HR?
.45
XF
1
0.00
.13
RO —
28
1.46
.74
SG
2
0.30
.26
UA
5
0.70
.42
XH
1
0.00
.13
RD
17
1.23
.64
SL
2
0.30
.25
UI—
5
0.70
.42
XN
1
0.00
.13
RP
13
1.11
.59
SK.
1
.13
UM
5
0.70
.42
X0„_
1
0.00
.13
RR —
11
1.04
.56
SV__
1
.13
UB
3
0.48
.33
XR—
1
0.00
.13
RC
9
0.95
.53
SY
1
.13
UC—
3
0.48
.33
XS—
1
0.00
.13
RM
9
0.95
.53
UD
3
0.48
.33
RY
9
0.95
.53
TH
78
1.89
.92
UP....
2
0.30
.25
YT
15
1.18
.62
RG
7
0.85
.48
TE
71
1.85
.91
UF
1
0.00
.13
YF
11
1.04
.56
RN
7
0.86
.48
TO
50
.84
UO_...
1
0.00
.13
YS
11
1.04
.56
RF
6
0.78
.45
TI
45
1.65
.82
UV....
1
0.00
.13
YO
10
1.00
.55
RL
5
0.70
.42
TY
41
1.61
.80
YE
9
0.95
.53
RU
5
.42
TW
36
1.56
.78
VE—
57
1.76
.87
YA
6
0.78
.45
RV
5
0.70
.42
TA
28
1.45
.74
VI....
12
1.08
.58
YN—
6
0.78
.45
Rff
4
.38
TS
19
1.28
.67
VA....
6
0.78
.45
YC
4
0.60
.38
RH
3
EES
.33
TT
19
1.28
.67
VO....
1
0.00
.13
YD
4
0.60
.88
RB
2
rm
.25
TR
17
1.23
.64
VT....
1
0.00
.13
YR
4
0.60
.38
RJ
1
.13
TF
7
0.85
.48
YI
3
0.48
.33
RK
1
.13
TN.
7
0.85
.48
WE....
22
1.34
.69
YP
8
0.48
.33
■
TC
6
0.78
.45
WO....
19
1.28
.67
YB
2
0.30
.26
ST
63
.88
TD
6
0.78
.45
WI__
13
1.11
.59
YL
2
0.30
.25
SE
49
1.69
.84
TM....
6
0.78
.45
WA—
12
1.08
.58
YM
2
0.30
.25
SI
34
1.53
.77
TL....
5
.42
WH....
4
0.60
.38
YG
1
0.00
.13
SH
26
1.41
.72
TU
5
.42
WN....
2
0.30
.25
YH
1
0.00
.13
SA
24
1.38
.71
TB
3
0.48
.33
WL....
1
0.00
.13
YU
1
0.00
.13
SS
19
1.28
.67
TP
2
ESQ
.25
WR....
1
0.00
.13
YW
1
0.00
.13
SO
16
1.18
.62
TG.
1
f 2
.13
WS....
1
0.00,
.13
SC.._
13
1.11
.59
TQ
1
.13
WY....
1
0.00
.13
ZE
2
0.30
.25
SF
12
.58
TZ
1
.13
ZA
1
0.00
.13
SU
11
.56
XT....
7
0.85
.48
ZI.
1
0.00
.13
SP
10
.55
UR—
31
1.49
.75
XA....
2
0.30
.25
S.000
SD
5
.42
UN—
21
1.32
.68
XC....
2
0.30
.25
1 For arrangement alphabetically first under initial letters and then under final letters, see Table 6-A.
2-21
Table' 9-*A . — The 428 different digraphs of Table 6-A, 'arranged first alphabetically according to
their final letters and then according to their absolute frequencies, accompanied by the logarithms
of their assigned probabilities
F
Li,(F)
Li324
(2F)
F
Lio(F)
MaSai
F
Lw(F)
Lim
(2F)
F
Lio(F)
LlM
<2F)
RA
39
1.59
.80
EC
32
MB
.76
RE....
98
1.99
.96
GF
2
0.30
.25
MA
36
1.56
.78
IC.„.
22
.69
TE....
71
1.85
.91
PF
2
0.30
.25
EA....
35
1.54
.78
NC
19
Ej
.67
NE....
57
1.76
.87
CF_...
1
0.00
.13
DA
32
1.61
.76
AC
14
1.15
.61
VE....
57
1.76
.87
MF
1
0.00
.13
LA
28
1.45
.74
SC....
13
1.11
.59
SE
49
1.69
.84
UF
1
0.00
.13
TA
28
1.45
.74
RC....
9
0.95
.53
EE....
42
1.62
.81
XF
1
0.00
.13
NA
26
1.41
.72
OC.„.
8
0.90
.51
LE
37
1.57
.79
SA
24
1.38
.71
TC....
6
0.78
.45
DE....
33
1.52
.77
CA..„
20
1.30
.67
DC r ...
4
0.60
.38
CE
32
1.51
.76
NG
27
1.43
.73
HA
20
1.30
.67
YC
4
0.60
.38
ME....
26
1.41
.72
IG
19
1.28
.67
PA
14
1.15
.61
cc....
3
0.48
.33
PE....
23
UG—
8
0.90
.51
WA„.„
12
1.08
.58
HC....
3
0.48
.33
WE....
22
1.34
.69
RG
7
0.85
.48
IA
8
0.90
.51
LC....
3
0.48
.33
HE....
20
AG....
6
0.78
.45
GA
7
0.85
.48
MC
3
0.48
.33
BE....
18
1.26
.66
EG....
4
0.60
.38
0A..„
7
0.85
.48
uc....
3
0.48
.33
GE
14
1.15
DG..._
2
0.30
.25
VA
6
0.78
.45
FC_...
2
0.30
.25
IE....
13
1.11
.59
OG....
2
0.30
.25
YA
6
0.78
.45
GC....
2
0.30
.25
UE....
11
.66
SG....
2
0.30
.25
FA
6
0.70
.42
XC.._
2
0.30
.25
FE
10
.55
FG....
1
0.00
.13
UA
5
0.70
.42
KC..._
1
0.00
.13
YE....
9
0.95
GG....
1
0.00
.13
BA
4
0.60
.38
PC.._
1
0.00
.13
KE....
6
0.78
.45
LG....
1
0.00
.13
AA
3
0.48
.33
OE....
3
0.48
.33
TG....
1
0.00
.13
XA
2
0.30
.25
JE....
2
0.30
YG....
1
0.00
.13
JA
1
0.00
.13
ED....
60
1.78
.88
ZE
2
0.30
KA
1
0.00
.13
ND
52
1.72
.85
AE
1
.13
ZA
1
0.00
.13
AD
27
1.43
.73
XE
1
.13
RD
17
1.23
.64
TH....
78
1.89
.92
AB_.„
6
0.78
.45
OD....
12
1.08
.58
SH....
26
1.41
.72
MB....
6
0.78
.45
LD....
9
0.95
.53
GH....
20
1.30
.67
DB
4
0.60
.38
DD
8
0.90
.51
OF....
25
.72
CH_...
14
1.15
.61
EB
4
0.60
.38
ID
6
0.78
.45
EF___.
18
1.26
. 66
EH....
7
0.85
.48
OB
4
0.60
.38
TD
6
0.78
.45
SF.___
12
.58
NH....
4
0.60
.38
LB....
3
0.48
.33
SD
5
0.70
.42
FF....
11
.56
WH....
4
0.60
.38
SB....
3
0.48
.33
YD....
4
0.60
.38
YF....
11
.56
OH....
3
0.48
.33
TB....
3
0.48
.33
UD....
3
0.48
.33
IF—
10
.65
PH....
3
0.48
.33
UB..„
3
0.48
.33
HD....
2
0.30
.25
NF—
9
0.95
.53
RH..._
3
o.4a
.33
IB....
2
0.30
.25
CD....
1
0.00
.13
DF—
8
0.90
.51
AH....
2
0.30
.25
NB
2
0.30
.25
FD_...
1
0.00
.13
TF—
7
0.85
.48
DH....
2
0.30
.25
RB
2
0.30
.25
GD
1
0.00
.13
RF
6
0.78
.45
LH....
1
0.00
.13
YB
2
0.30
.25
MD
1
0.00
.13
HF
5
39
.42
MH....
1
0.00
.13
HB..._
1
0.00
.13
PD
1
0.00
.13
AF
4
IB
.'38
XH—
1
O.OOi
.13
PB
1
0.00
.13
XD.__.
1
0.00
.13
LF
3
m
.33
YH....
1
0.00
.13
2-22
RESTRICTED
REF ID: A5 68 95
Table 9-A, Contd . — The 428 different digraphs of Table 6-A, arranged first alphabetically accord-
ing to their final letters and then according to their absolute frequencies, accompanied by the
logarithms of their assigned probabilities
REF ID : A56895
REDTRIOTED
Table 9-A, Concluded . — The b 28 different digraphs of Table 6-A, arranged first alphabetically,
according to their final letters and then according to their absolute frequencies, accompanied by
the logarithms of their assigned probabilities
REF ID: A5 68 95
Table 9-B. — The 18 digraphs composing 25% of the 5,000 digraphs of Table 6-A, accompanied by
the logarithms of their assigned probabilities, arranged alphabetically according to their final letters
(1) AND ACCORDING TO THEIR INITIAL (2) AND ACCORDING TO THEIR ABSOLUTE
LETTERS FREQUENCIES
F
L»(F)
BBEM 1
F
Lio(F)
WISH
Kin
F
Lio(F)
Kw
F
L»(F)
Lac
(2F)
ED
60
1.78
.88
IN....
75
1.88
.92
ED....
60
1.78
.88
IN....
75
1.88
.92
ND....
52
1.72
.85
ON....
77
1.89
.92
ND-.
52
1.72
.85
AN..~
64
1.81
.89
NE
67
1.76
.87
TO....
50
1.70
.84
RE....
98
1.99
.96
TO....
60
1.70
.84
RE....
98
1.99
.96
87
1.94
.94
TE
71
1.85
.91
87
1.94
.94
SE_...
49
1.69
.84
ER....
NE....
57
1.76
.87
ER....
TE....
71
1.85
.91
OR....
64
1.81
.89
VE....
57
1.76
.87
OR....
64
1.81
. 89
VE....
57
1.76
.87
54
.86
SE....
49
1.69
.84
1.73
.86
ES....
1.73
ES
54
TH....
78
1.89
.92
NT....
82
1.91
.93
TH
78
1.89
.92
NT
82
1.91
.93
ST....
63
1.80
.88
ST
63
1.80
.88
AN....
64
1.81
.89
1 ,
249
EN
111
2.05
.99
1 ,
249
EN....
111
2.05
.99
ON
77
1.89
.92
Table 9-C . — The 68 digraphs composing 50% of the 5,000 digraphs of Table 6-A, accompanied by
the logarithms of their assigned probabilities, arranged alphabetically according to their final letters
RESTRICTED
REF ID: A5 68 95
Table 9-C, Concluded . — The 53 digraphs composing 50% of the 5,000 digraphs of Table 6-A,
accompanied by the logarithms of their assigned probabilities, arranged alphabetically according to
their final letters
(2) AND ACCORDING TO THEIR ABSOLUTE FREQUENCIES
F
Ino(F)
mym
msm
L»(F)
mmm
BMlIl
L«(F)
WMffm
F
LioOF)
Lim
m
RA.
39
1.59
.80
EE
42
.81
en..„:
111
2.05
.99
ES..„
54
Ml
.86
MA
86
1.66
.78
LE
37
1.57
.79
ON....
77
1.89
.92
AS
41
.80
EA
35
1.54
.78
DE
33
1.52
.77
IN
75
1.88
.92
IS....
35
■Wfrl
.78
DA
32
1.51
.76
CE
32
1.51
.76
AN....
64
1.81
.89
RS....
31
1.49
.75
LA....
28
1.45
.74
i
TA.»„
28
1.45
.74
TH
78
1.89
.92
TO....
60
1.70
.84
NT....
ST
82
63
1.91
1.80
.93
.88
EC
32
1.61
.76
TI
45
1.65
.82
CO....
41
1.61
.80
AT
47
1.67
.83
10 ....
41
1.61
.80
RT....
42
1.62
.81
ED....
60
1.78
.88
FI....
39
1.59
.80
FO....
40
1.60
.80
ET....
37
1.57
.79
ND
52
1.72
.85
SI....
34
1.53
.77
RO....
28
1.45
.74
HT
28
1.45
.74
HI....
33
1.52
.77
RE
98
1.99
.96
NI
30
1.48
.75
OU
37
1.57
.79
TE
71
1.85
.91
RI
30
1.48
.75
ER....
87
1.94
.94
TW
36
1.56
.78
NE....
57
1.76
.87
OR....
64
1.81
.89
VE....
57
1.76
.87
AL
32
1.51
.76
AR
44
1.64
.82
TY....
41
1.61
.80
SE
49
1.69
.84
EL....
29
1.46
.74
UR
31
1.49
.75
2,495
Table 9-D. — The 122 digraphs composing 75% of the 5,000 digraphs of Table 6-A, accompanied by
the logarithms of their assigned probabilities, arranged alphabetically according to their final letters
(1) AND ACCORDING TO THEIR INITIAL LETTERS
F
L»(F)
F
Li*(F)
HPSH
BH
F
Lio(F)
mm
jasmin:
L»(F)
Lim
(2F)
CA 20
DA.... 32
EA 35
HA.... 20
LA.... 28
MA.... 36
NA 26
PA 14
RA.... 39
SA.... 24
TA.... 28
AC. ... 14
EC 32
IC.... 22
NC.... 19
AD. ... 27
ED.... 60
1.30
1.61
1.54
1.30
1.45
1.56
1.41
1.15
1.59
1.38
1.45
1.15
1.51
1.34
1.28
1.43
1.78
.67
.76
.78
.67
.74
.78
.72
.61
.80
.71
.74
.61
.76
.69
.67
.73
.88
ND 52
RD 17
BE.... 18
CE.... 32
DE.... 33
EE.... 42
GE.... 14
HE.... 20
IE.... 13
LE.... 37
ME.... 26
NE.... 57
PE.... 23
RE.... 98
SE.... 49
TE.... 71
VE.... 57
WE 22
1.72
1.23
1.26
1.51
1.52
1.62
1.15
1.30
1.11
1.57
1.41
1.76
1.36
1.99
1.69
1.85
1.76
1.34
.85
.64
.66
.76
.77
.81
.61
.67
.59
.79
.72
.87
.70
.96
.84
.91
.87
.69
EF 18
OF 25
IG 19
NG 27
CH — 14
GH 20
SH — 26
TH 78
1
AI 17
DI 27
El 27
FI 89
HI 33
LI 20
NI 30
RI 30
1.26
1.40
1.28
1.43
1.15
1.30
1.41
1.89
1.23
1.43
1.43
1.59
1.52
1.30
1.48
1.48
.66
.72-
.67
.73
.61
.67
.72
.92
.64
.73
.73
.80
.77
.67
.75
.75
SI__ 34
TI.... 45
AL. ... 32
EL. '... 29
IL 23
LL.._. 27
OL. .._ 19
AM. ... 14
EM. ... 14
OM. ... 25
AN. ... 64
EN. -111
IN.... 75
ON. ... 77
UN 21
1.53
1.65
1.51
1.46
1.36
1.43
1.28
1.15
1.15
1.40
1.81
2.05
1.88
1.89
1.32
.77
.82
.76
.74
.70
.73
.67
.61
.61
.72
.89
.99
.92
.92
.68
2-26
RESTRICTE D
REF ID: A56895
Table 9-D, Could.— The 122 digraphs composing 75% of the 5,000 digraphs of Table 6-A, ac-
companied by the logarithms of their assigned probabilities, arranged alphabetically according to
their final letters
(1) AND ACCORDING TO THEIR INITIAL LETTERS— Concluded
Lu(F)
41 l.
16 1.
40 1.
20 1 .
41 1.
13 1.
18 1.
17 1.
28 1.
16 1.
50 1.
19 1.
61 .80
20 .63
60 .80
30 .67
61 .80
11 .59
26 .66
23 .64
45 .74
18 .62
70 .84
28 .67
20 1.30 .67
25 1.40 .72
44 1.64 .82
87 1.94 .94
17 1.23 .64
1.. .. 27 1.43 .73
64 1.81 .89
1.. .. 18 1.26 .66
17 1.23 .64
1.... 31 1.49 .75
5 41 1.61 .80
3 13 1.11 .59
3 64 1.73 .86
3 35 1.54 .78
3 24 1.38 .71
3 — 14 1.15 .61
31 1.49 .75
19 1.28 .67
19 1.28 .67
.67 .83
,15 .61
.18 .62
.57 .79
.45 .74
.43 .73
.91 .93
.28 .67
.62 .81
,80 .88
TT 19
YT 15
AU 13
OU.„. 37
QU 15
EV 20
IV.... 25
TW 36
IX.... 15
TY 41
3,745
1.11 .59
1.57 .79
1.18 .62
1.30 .67
1.40 .72
1.56 .78
1.18 .62
1.61 .80
(2) AND ACCORDING TO THEIR ABSOLUTE FREQUENCIES
Lu(F)
.99 .96
.85 .91
.76 .87
.76 .87
,69 .84
.62 .81
.57 .79
.52 .77
.61 .76
.41 .72
.36 .70
.34 .69
.30 .67
.26 .66
.15 .61
.11 .59
25 1.40 1 .72
18 1.26
|HQ
Li 0 (F)
■luM
F
Lio(F)
TH...
78
1.89
.92
OM
25
1.40
.72
SH...
26
1.41
.72
AM....
14
1.15
.61
GH...
20
1.30
.67
EM....
14
1.15
.61
CH...
14
1.16
.61
EN
111
2.05
.99
TI_.
FI...
SI...
HI...
45
39
34
33
1. 65
1.59
1.53
1.52
.82
.80
.77
.77
ON....
IN....
AN....
UN....
77
75
64
21
1.89
1.88
1.81
1.32
.92
.92
.89
.68
NI...
RI
DI
El
LI_.
AI...
30
30
27
. 27
. 20
. 17
1.48
1.48
1.43
1.43
1.30,
1.23
.75
.75
.73
.73
.67
.64
TO....
CO....
10 ....
FO._._
RO_._.
HO....
60
41
41
40
28
20
1.70
1.61
1.61
1.60
1.45
1.30
.84
.80
.80
.80
.74
.67
WO....
19
1.28
.67
AL...
. 32
1.51
.76
NO....
18
1.26
.66
EL...
. 29
1.46
.74
PO....
17
1.23
. 64
LL...
. 27
1.43
.73
DO....
16
1.20
.63
IL._.
. 23
1.36
.70
SO....
16
1.18
.62
OL...
. 19
1.28
.67
LO
13
1.11
.59
NG 27 1.43 .73
IG 19 1.28 .67
RESTRICTED
REF ID : A56895
Table 9-D, Concluded . — The 122 digraphs composing 75% of the 5,000 digraphs of Table 6-A,
accompanied by the logarithms of their assigned probabilities, arranged alphabetically according to
their final letters
(2) AND ACCORDING TO THEIR ABSOLUTE FREQUENCIES -Concluded
F
LioCF)
Lm
(2F)
F
Lio(F)
Liii
(2F)
F
Lta(F)
1*4 •
(2F)
F
LioCF)
1*4
(2F)
OP.„„
25
1.40
.72
ES....
54
1.73
.86
NT....
82
1.91
.93
ou....
37
m
.79
EP
20
1.30
.67
AS....
41
1.61
.80
ST....
63
.88
QU....
15
.62
IS....
35
1.64
.78
AT....
47
1.67
.83
AU
13
ESQ
.59
RS
31
1.49
.76
RT
42
1.62
.81
IV....
EV
25
20
1.40
1.30
.72
.67
ER
87
1.94
.94
NS....
24
1.38
.71
ET
37
1.67
.79
OR
64
1.81
.89
SS....
19
1.28
.67
HT....
28
1.45
.74
AR
44
1.64
.82
TS....
19
1.28
.67
IT....
27
1.43
.73
TW
36
1.56
.78
UR
31
1.49
.75
OS....
14
1.15
.61
OT
19
1.28
.67
IX
15
1.18
.62
IR
27
1.43
.78
DS....
13
1.11
.59
TT
19
1.28
.67
PR....
18
1.26
. 66
DT
15
1.18
.62
TY
41
1.61
.80
HR....
17
1.23
.64
YT....
15
1.18
.62
3.745
so
i
■
■
17
1.23
.64
CT
14
1.15
.61
i
Table 9-E . — All the 128 different digraphs of Table 6-A, arranged alphabetically first according to
their final letters and then according to their initial letters
(SEE TABLE 6-A.— READ DOWN THE COLUMNS)
Table 10-A . — The 56 trigraphs appearing 100 or more times in the 50,000 letters of Governmental
plain-text telegrams, arranged according to their absolute frequencies, accompanied by the loga-
rithms of their assigned probabilities
F
LioCF)
wmszmm
F
Lii(F)
(2F)
F
Lu(F)
Inn
(2P)
ENT
569
2.76
.99
TOP
.... 174
2.24
.82
EIG
_.. 135
rm
.79
ION
260
2.41
.88
NTH
.... 171
2.23
.82
FIV
.... 135
2.13
.79
AND
228
2.36
.86
TWE.
wSFf i
2.23
.82
MEN
.... 131
2.12
.78
ING
226
2.35
.86
TWO
2.21
.81
SEV
.... 131
2.12
.78
IVE
225
2.35
.86
ATI
iSEi
2.20
.81
ERS
.... 126
Ptlil
.78
TTO
221
2.34
.85
THR
_.. 158
2.20
.81
UNO
wmm
2.10
.78
FOR
218
2.34
.86
NTY
2.20
.81
NET
.... 118
rm
.77
nilR
211
2.32
.85
HRE
mm
2.18
.80
PER.
.... 115
2.06
.76
THI
211
2.32
.85
WEN.. ..
n£|&]
2.18
.80
STA.
.... 115
.76
ONE
210
2.32
.85
FOU
.... 152
2.18
.80
TER
.... 1 Jr,
2.06
.76
NIN
207
2.32
.85
ORT
.... 146
2.16
.80
EQU
.... Ill
.76
STO
202
2.31
.84
REE
.... 146
2.16
.80
RED
.... 113
.76
EEN
196
2.29
.84
SIX.
.... 146
2.16
.80
TED
.... 112
.76
ght
196
2.29
.84
ASH......
.... 143
2.16
.80
ERI
BE m
.76
INE
192
2.28
.83
DAS
■El
2.15
.79
HIR.
.75
VEN
190
2.28
.83
IGH.
•
2.15
.79
IRT
.76
EVE
177
2.25
.82
ERE
.... 138
2.14
.79
DER
.74
EST...,.
176
2.25
.82
COM
.... 136
2.13
.79
DRE......
.74
TEE
174
2.24
.82
ATE
.... 135
2.13
.79
•
2-28
RESTRICTED
REF ID : A56895
RESTRICTE D-
Table 10~B. — The 56 trigraphs appearing 100 or more times in the 50,000 letters of Governmental
plain-text telegrams, arranged first alphabetically according to their initial letters, and then
according to their absolute frequencies, accompanied by the logarithms of their assigned probabilities
p
L»(F)
Ian
(2F)
F
Lm(F)
Kl
mml
AND
228
2.36
.86
GHT
196
2.29
.84
ATI
2.20
.81
ASH
143
2.16
.80
HRE
153
2.18
.80
ATE
136
2.13
.79
HIR
106
2.03
.75
COM
136
2.13
.79
TOM
260
2.41
.88
ING
226
2.35
.86
DAS
2.15
.79
IVE
225
2.35
.86
DER
101
2.00
.74
INE
192
2.28
.83
DRE„
HiTil
2.00
.74 .
TGH
140
2.15
.79
IRT
105
2.02
.76
ENT
569
2.76
.99
EEN
196
2.29
.84
MEN..
131
2.12
.78
FIVE
177
2.25
.82
EST
176
2.25
.82
NIN
207
2.32
.85
ERE
138
2.14
.79
NTH
171
2.23
.82
EIG
135
NTY
157
2.20
.81
ERS
126
2.10
.78
NET
118
2.07
.77
EQU
114
2.06
.76
ERI
109
2.04
.76
OUR
211
2.32
.85
ONE
210
2.32
.85
FOR
218
2.34
.85
ORT
146
2.16
.80
FOU
152
2.18
.80
FIV
136
2.13
PER
115
2.06
.76
Ln(F)
Lilt
(2F)
REE-
RED.
TIO.
THI.
TEE-
146
113
STO 202
SIX 146
SEV 131
STA 115
221
211
174
174
170
163
TOP
TWE
TWO
THR.. 158
TER 116
TED___:__ 112
UND 125
VEN ,_1 190
WEN_ 153
2.16
2.05
2.31
2.16
2.12
2.06
2.34
2.32
2.24
2.24
2.23
2.21
2.20
2.06
2.05
2.10
2.28
2.18
.80
.76
.84
.80
.78
.76
.85
.85
.82
.82
.82
.81
.81
.76
.76
.78
.83
.80
Table 10-C . — The 56 trigraphs appearing 100 or more times in the 50,000 letters of Governmental
plain-text telegrams, arranged first alphabetically according to their central letters, and then ac-
cording to their absolute frequencies, accompanied by the logarithms of their assigned probabilities
F 1
LloCF)
SIS
DA S
140
2.15
.79
IGH
140
EEN
196
2.29
.84
VEN
190
2.28
.83
TEE
174
2.24
.82
THI
211
WEN
153
2. J8
.80
GHT
196
REE-
146
2.16
.80
THR
168
MEN
131
2.12
.78
SEV
131
2.12
.78
NET _
118
2.07
.77
Tin
221
PER
115
2.06
.76
NTN
207
TER
115
2.06
.76
SIX
146
RED
113
2.05
.76
EIG
135
TED
112
2.05
.76
EIV
135
DER
101
2.00
.74
HTR
106
2-29
KSv-
Lm(F)
wjm
.79
ENT
569
2.76
.99
AND
228
2.36
.86
ING
226
2.35
.86
2.32
.85
ONE
210
2.32
.85
2.29
.84
INE
192
2.28
.83
2.20
.81
UND
125
2.10
■
.78
2.34
.85
2.32
.85
ION
260
2.41
.88
2.16
.80
FOR
218
2.34
.85
2.13
.79
TOP
174
2.24
.82
2.13
.79
FOU
152
2.18
.80
.75
COM
136
2.13
.79
RESTRICTED -
Tablb 10-C, Concluded . — The 66 trigraphs appearing 100 or more times in the 50,000 letters of
Governmental plain-text telegram, arranged first alphabetically according to their central letters,
and then according to their absolute frequencies, accompanied by the logarithms of their assigned
probabilities
F
L»(F)
1*4
(2F)
F
Ln(F)
(2F)
F
Lio(F)
rxsr
(2F)
EQU..
.. 114
2.06
.76
EST
.... 176
2.25
.82
OUR
.... 211
2.32
.85
ASH
.... 143
2.16
.80
HRE
.. 158
2.18
.80
ORT
.. 146
2.16
.80
STO
.... 202
2.31
.84
IVE
.... 225
2.35
.86
ERE
.. 188
2.14
.79
NTH.
.... 171
2.28
.82
EVE
.... 177
2.25
.82
ERS
.. 126
2.10
.78
ATI.
.... 160
2.20
.81
ERI
.. 109
2.04
.76
NTY.
.... 157
2.20
.81
IRT
.. 105
2.02
.75
ATE.
.... 135
2.13
.79
TWE
.... 170
2.23
.82
DRE
„ 100
2.00
.74
STA......
.... 115
2.06
.76
TWO
.... 163
2.21
.81
Table 10-D . — The 66 trigraphs appearing 100 or more times in the 50,000 letters of Governmental
plain-text telegrams, arranged first alphabetically according to their final letters, and then according
to their absolute frequencies, accompanied by the logarithms of their assigned probabilities
RE3TIUCTE B
REF ID: A5 68 95
RESTRICTED
Table 11-A.- — The 5i tetragraphs appearing 50 or more times in the 50,000 letters of Governmental
plan-text telegrams, arranged according to their absolute frequencies, accompanied by the logarithms
of their assigned probabilities _____
F
Lu(F)
L»4
(2F)
F
Lw<F)
.
mni
mmmm
F
7MF)
Wfrm
B35l
TION
218
2.34
.99
THIR
.._ 104
2.02
.87
ASHT
64
1.81
.79
EVEN
168
2.23
.95
EENT
.... 102
2.01
.87
HUND
64
1.81
.79
TEEN
163
2.21
.94
REQU....
.... 98
1.99
.86
DRED
63
.79
ENTY
161
2.21
.94
HIRT
.... 97
1.99
.86
RIOD
63
.79
STOP
154
2.19
.93
COMM....
.... 93
1.97
.85
IVED
62
1.79
.78
WENT
153
2.18
.93
QUES....
.... 87
1.94
.84
ENTS
62
.78
NINE
153
2.18
.93 .
UEST
.... 87
1.94
.84
FFIC
62
1.79
.78
TWEN
152
2.18
.93
EQUE....
.... 86
1.93
.84
FROM
59
1.77
.78
THRE
149
2.17
.93
NDRE..-.
.. 77
1.89
.82
IRTY
59
1.77
.78
FOUR
144
2.16
.92
OMMA
.... 71
1.85
.81
RTEE
59
1.77
.78
IGHT
140
2.15
.92
LLAR
.... 71
1.85
.81
UNDR
.59
1.77
.78
FIVE
186
2.13
.91 !
OLLA....
.... 70
1.85
.81
NAUG
56
1.76
.77
HREE
134
2.18
.91
VENT....
.... 70
1.85
.81
OURT
56
1.75
.77
DASH
132 1
2.12
.91
DOLL....
.... 68
1.83
.80
UGHT
56
1.75
.77
EIGH
132
2.12
.91
LARS....
.... 68
1.83
.80
STAT
54
1.7$
.76
SEVE
121
2.08
.89
THIS....
.... 68
1.83
.80
AUGH
52
1.72
•i 6
ENTH
114
2.06
.89
PERI....
67
1.83
.80
CENT
52
1.72
• 76
MENT
111
2.05
.88
ERIO
.._ 66
1.82
.80
FICE
50
1.70
.76
Table 11-B. — The 5J f tetragraphs appearing BO or more times in the 50,000 letters of Governmental
plain-text telegrams, arranged first alphabetically according to their initial letters, and then ac-
cording to their absolute frequencies, accompanied by the logarithms of their assigned probabilities
F
Lio(F)
Lz?<
(2F)
|
Lio(F)
m&mm
! F
1
Lu(F)
HS31
ASHT.* 64
AUGH 62
COMM 93
CENT 52
DASH 132
DOLL 68
DRED 63
EVEN 168
ENTY 161
EIGH 132
ENTH 114
EENT 102
EQUE 86
ERIO 66
ENTS 62
FOUR 144
FIVE 136
FFIC 62
FROM 59
FICE 50
1.81
1.72
1.97
1.72
2.12
1.83
1.80
2.23
2.21
2.12
2.06
2.01
1.93
1.82
1.79
2.16
2.13
1.79
1.77
1.70
.79
.76
.85
.76
.91
.80
.79
.95 *
.94
.91
.89 j
.87 |
.84
.80
.78 1
.92
.91
.78
.78
.75 •
HREE 134
HIRT 97
1 HUND 64
IGHT 140
IVED 62
IRTY 69
LLAR 71
LARS 68
MENT 111
NINE 163
NDRE 77
NAUG 56
OMMA 71
OLLA 70
OURT 56
PERI 67
QUES 87
2.13
1.99
1.81
2.15
1.79
1.77
1.85
1.83
2.06
2.18
1.89
1.76
1.85
1.85
1.75
1.83
1.94
.91
.86
.79
.92
.78
.78
.81
.80
.88
.93
.82
.77
.81
.81
.77
.80
.84
REQU 98
RIOD 63
RTEE 59
STOP 154
SEVE 121
STAT 54
TION 218
TEEN 163
TWEN 152
THRE 149
THIR 104
THIS 68
UEST 87
UNDR 69
UGHT 66
VENT 70
WENT 153
'1.99
1.80
1.77
2.19
2.08
1.73
2.34
2.21
2.18
2.17
2.02
1.83
1.94
1.77
1.75
1.85
2.18
.86
.7:9
.7,8
.89
.76
.99
.94
.93
.93
.87
.80
.84
.78
.77
.81
.93
2-31
RESTRICTED
RESTRICTED
REF ID: A5 68 95
Table 11-C. — The 5k tctragraphs appearing 50 or more times in the 50,000 letters of Governmental
plain-text telegrams, arranged first alphabetically according to their second letters, and then ac-
cording to their absolute frequencies, accompanied by the logarithms of their assigned probabilities
p
L»(F)
Lm
<2F)
P
Lu(F) |
mjsmm
P
Lm(F)
HCST
(ZF)
DASH 132
LARS 68
NAUG 56
NDRE 77
TEEN 163
WENT 153
SEVE 121
MENT 111
EENT 102
REQU 98
UEST 87
VENT 70
PERI 67
CENT 52
FFIC 62
IGHT 140
UGHT 56
THRE 149
THIR 104
THIS 68
2.12
1.83
1.75
1.89
2.21
2.18
2.08
2.05
2.01
1.99
1.94
1.85
1.83
1.72
1.79
2.15
1.75
2.17
|2.02
1.83
.91
.80
.77
.82
.94
.93
.89
.88
.87
.86
.84
.81
.80
.76
.78
.92
.77
.93
.87
.80
TION 218
NINE 153
FIVE 136
EIGH 132
HIRT 97
RIOD 63
FICE 60
LLAR 71
OLLA 70
OMMA 71
ENTY 161
ENTH 114
ENTS.. „ 62
UNDR 59
FOUR 144
COMM 93
DOLL 68
EQUE 86
2.34
2.18
2.18
2.12
1.99
1.80
1.70
1.85
1.85
1.85
2.21
2.06
1.79
1.77
2.16
1.97
1.83
1.93
.99
.93
.91
.91
.86
.79
.75
.81
.81
.81
.94
.89
.78
.78
.92
.85
.80
.84
HREE 134
ERIO 66
DRED 63
FROM 59
IRTY..„1._ 59
ASHT 64
STOP 154
RTEE 59
STAT 54
QUES 87
HUND 64
OURT 56
AUGH. 62
EVEN 168
IVED 62
TWEN 162
2.13
1.82
1.80
1.77
1.77
1.81
2.19
1.77
1.78
1.94
1.81
1.76
1.72
2.23
1.79
2.18
.91
.80
.79
.78
.78
.79
.93
.78
.76
.84
.79
.77
.76
.95
.78
.93
Table 11-D. — The 5k tetragraphs appearing 50 or more times in the 50,000 letters of Governmental
plain-text telegrams, arranged first alphabetically according to their third letters, and then according
to their absolute frequencies, accompanied by the logarithms of their assigned probabilities
P
Lu(F)
»*r?i
LLAR
71
1.85
.81
STAT
54
1.73
.76
FICE
50
1.70
.76
UNDR
59
1.77
00
EVEN
168
2.23
.95
TEEN.
163
2.21
.94
TWEN
152
2.18
.93
HREE
134
2.13
.91
QUES
87
1.94
.84
DRED
63
1.80
.79
IVED
62
1.79
.78
RTEE
59
1.77
.78
P
LiaCF)
LiU4
(2F)
EIGH
182
2.12
.91
AUGH
52
1.72
.76
IGHT
140
2.15
.92
ASHT
64
1.81
.79
UGHT
56
1.75
.77
THIR
104
2.02
.87
THIS
68
1.83
.80
ERIO
66
1,82
.80
FFIC
62
1.79
.78
COMM 93
OMMA 71
WENT 153
NINE 153
MENT 111
EENT 102
VENT 70
HUND 64
CENT 52
TION 218
STOP 154
RIOD 63
FROM 59
L»(F)
1.97
1.85
2.18
2.18
2.05
2.01
1.85
1.81
1.72
2.34
2.19
1.80
1.77
(ZF)
.85
.81
.93
.93
.88
.87
.81
.79
.76
.99
.93
.79
.78
OLLA
DOLL.
70 1.85 .81
68 1.83 .80
REF ID: A5 68 95
Table 11-D, Concluded . — The 5U tetragraphs appearing 50 or more times in the 50,000 letters of
Governmental plain-text telegrams, arranged first alphabetically according to their third letters, and
then according to their absolute frequencies, accompanied by the logarithms of their assigned
probabilities
F
Lw(F)
K« 1
F
Llfl(F)
Dm
(2F)
REQU
..... 98
1.99
00
Oi
DASH
132
2.12
.91
UEST
87
1.94
.84
THRE_„
.... 149
2.17
.93
HIRT...
.._ 97
1.99
.86
NDRE...
.... 77
1.89
.82
ENTY
161
2.21
.94
LARS...
68
1.83
.80
ENTH
114
2.06
.89
PERI...
.... 67
1.83
.80
ENTS
62
1.79
.78
OURT...
..... 56
1.75
.77
IRTY
59
1.77
.78
FOUR 144 2.16 .92
EQUE 86 1.93 .84
NAUG 56 1.76 .77
FIVE 135 2.13 .91
SEVE 121 2.08 .89
Table 11-E. — The 5$. tetragraphs appearing 50 or more times in the 50,000 letters of Governmental
plain-text telegrams, arranged first alphabetically according to their final letters, and then according
to their absolute frequencies, accompanied by the logarithms of their assigned probabilities
P Lu(F)
OMMA..
OLLA..
FFIC 62 1.79 .78
HUND 64 1.81 .79
DRED 63 1.80 .79
RIOD 63 1.80 .79
IVED 62 1.79 .78
NINE 153
THRE 149
FIVE 135
HREE 134
SEVE 121
EQUE 86
NDRE 77
RTEE 59
FICE 50
2.18 .93
2'. 17 .93
2.13 .91
2.13 .91
2.08 .89
1.93 .84
1.89 .82
1.77 .78
1.70 .75
DASH 132 2.12 .91
EIGH 132 2.12 .91
ENTH 114 2.06 .89
AUGH 52 1.72 .76
NAUG.
66 1.75 .77
PERI 67 1.83 .80
DOLL 68 1.83 .80
COMM 93 1.97 .85
FROM 59 1.77 .78
TION 218 2.34 .99
EVEN 168 2.23 .95
TEEN 163 2.21 .94
TWEN 152 2.18 .93
ERIO 66 1.82 .80
STOP 154 2.19 .93
FOUR 144 2.16 .92
THIR 104 2.02 .87
LLAR 71 1.85 .81
UNDR i 59 1.77 .78
P L»(F)
QUES 87 1.94 .84
THIS 68 1.83 .80
LARS 68 1.83 .80
ENTS 62 1.79 .78
WENT 153 2.18 .93
IGHT 140 2.15 .92
MENT 111 2.05 .88
EENT 102 2.01 .87
HIRT 97 1.99 .86
UEST 87 1.94 .84
VENT 70 1.85 .81
ASHT 64 1.81 .79
OURT 56 1.76 .77
UGHT 56 1.75 .77
STAT 54 1.73 .76
CENT 52 1.72 .76
REQU 98 1.99 .86
ENTY 161 2.21 .94
IRTY 59 1.77 .78
RESTRICTED
REF ID: A56895
Table 12. — Average length of words and messages
Number of
letters in
word
X
Number of
times K-letter
word appears
Number of
letters
i
378
378
2
973
1,946
3
1,307
3,921
4
1,635
6,540
5
1,410
7,050
6
1,143
6,858
7
1,009
7,063
8
717
5,736
9
476
4,284
10
274
2,740
11
161
1,771
12
86
1,032
13
23
299
14
23
322
15
4
60
9,619
50,000
(1 ) Average length of words 5.2 letters.
(2) Average length of messages. 217 letters.
(3) Modal (most frequent) length 105-114 letters.
(4) It is extremely unusual to find five consecutive letters without at least one vowel.
(6) The average number of letters between vowels is two.
2-34
nEDTRICTBfr
REF ID: A56895
RESTRICTED
Table 13. — Checkerboard individual frequencies 1
(Bnsotl on a count of 5,000 digraphs!
Pi Cx
A
B
C
D
E
244
225
375
394
197
F
G
H
I J
K
125
98
193
271
95
L
M
N
0
P
229
199
188
350
251
Q
R
S
T
U
148
162
268
427
295
V
W
X
Y
Z
42
12
34
91
97
212
317
368
308
249
A
B
C
D
E
120
108
216
256
85
F
G
H
I J
K
216
140
152
435
269
L
M
N
0
P
206
121
306
364
284
Q
R
S
T
U
38
29
21
147
43
V
W
X
Y
Z
C, P 2
1 The numbers in the Ci C 2 squares represent the frequency of the individual components of the cipher digraph
used to replace a given Pi P 2 digraph in accordance with a digraphic checkerboard system where Pi and P* are the
plain-text squares.
2-35
Fibst Letter
REF ID: A5 68 95
RESTRICTED
Table 14. — Relative logarithmic values of frequencies of English digraphs
[Based on a count of 5,000 digraphs. To obtain logarithm to base 10 (Log 10) divide by 100]
Second Letter
ABCDE FGHIJKLMNOPQRSTUVWXYZ
*In computations, assign a value of -100 as the log for these digraphs. These combinations do not usually
occur in 5,000 digraphs. Do not assign “0” to these combinations as that is the logarithmic value for a fre-
quency of one, and these combinations have a frequency of less than one.
REF ID: A5 68 95
Table 15. — Relative logarithmic values (. Log, 222) of frequencies of English digraphs '
[Based on a count of 6,000 digraphs]
Second Letter
ABCDEFGHIJKLMNOPQRSTUVWXYZ
* See pages 11-12 for details.
2-37
1197
I* L+r.
F.,n npr? th tt^d * * 'Etk'f f'D : A56895
SPECIAL-PURPOSE DATA
Table 16-A . — Frequency distribution of digraphs, based on 6h f 365
letters of decrypted U. S. Government messages in -which Z was used as
a word-separator and X was used for both Xp and Zp.
X* L+*j
ABCDBFOHXJKLMHOPQBSTUVWXTZ
*VV* k*' ** w** u* ^
In the text which gave rise to this and the following two tables, the
frequently-used punctuation signs "comma" and "period" were abbreviated
as CMA and PD, respectively, and the procedure term "repeat" was abbre-
viated as RET; thus, the digraphs CM, FD, PT, and RP, which usually do
not occur frequently (see Table 6- A), are of relatively high frequency
here .
2-38
REF ID: A5 68 95
7
~ REGTRICTED
Tabic l6-B ..—Frequency distribution of digraphs, based on the
text used for Table l6~A, from which the Z word- separator has been
omitted (total: 53 >866 letters)*
a-* Ltv.
A
B
C
D
E
F
G
II
X
J
K
L
M
n
0
p
Q
R
S
T
u
V
w
X
Y
Z
A
ns
no
141
to
134
III
24
131
it
SI
217
144
t31
SS
147
3
<S7
411
31S
4S
S8
to
zx
47
B
»t
1
Z
m
S
1
43
XZ
111
4
13
42
2
42
17
IX
IS
2
3
X
4o
C
g
El
H
043
m
gj
3
DO
B
313
II
S3
□
B
B
B
ISO
47
1
4
B
B
■
D
3
a
[2
n
307
s
i
7
a
9
xz
XX
ISI
17
14
It!
118
9
B
Q
m
B
B
■
E
3
□
3ft
tf|
41o
m
B
21
B
B
H
8SS
181
m
131
S3
B
BS
EQ
134
It
F
4o
□
B
2S
|Ol
Q
D
300
■3
i
31
2S
10
91
Q
B
m
B
□
9
9
1
3
7
>
G
loz
31
®1
244
n
fl
37
f
2
IX
10
tl
3
1
D
B
S3
38
fl
5
3
B
B
H
2?0
8
Q
fl
gg
S4
13
31
no
B
o
B!
fl
34
bj:
B
B
231
B!
yg
IS
X
□
□
B
I
84
□
PH
B
B
ra
330
8
S’
B
B
BS
B
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fli
fl
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B
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B
■
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a
B
B
Q
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21
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□
fl
S
B
B
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fl
B
B
7
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9
g
B
g
K
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B
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B
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B
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9
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B
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B
B
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fl
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333
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B
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B
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B
B
14
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72
g
£
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fl
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204
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B
B
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D
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B
B
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B
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B
84
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43
tit.
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til
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m
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£21
170
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fg
t
74
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II
•So
HI
X
m
B
36S
It
z
a
B
5“
Q
i
D
3
■
7
z
4
s
1
1
5“
II
8
Z
1
m
B
z
us
X
1
R
S3
131
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BS
H
B
it
207
n
to
41
1 4Z
SI
4X1
X41
fl
S3
a
E
fl
9
21
3o
7+
S
IBS
R]
B9
a
314
Itl
ss
4S3
9
■
11
zsr
4c
34
173
in
B
B
BH
SB
El
m
3t
z
43
T
277
30
U7
70
too
HI
21
sn
2
Q
14
t3
B
\m
443
HS
B
m
E3
a
B
2l
Xo
SI
U
48
B
m
9
m
7
41
c
B
|
+
S4
B
9
3S
m
B
1st
E
B
B
4
1
V
41
m
□
7
1
i
B
B
2
4
B
Q
2|
a
B
□
B
D
B
B
1
7
W
113
D
D
a
B
Z
B
B
IQ
□
fl
B
B
B
ffi
B
B
B
B
□
B
B
IS
t
X
liL
IS
m
B
B
D
B
□
E
B
B
B
o
B
B
B
B
H
□
B
St
3
Y
fl
B
m
B
Q
B
B
□
B
a
B
D
RJ
B
B
B
B
B
B
5J
B
n
IQ
I
IS
Z
r
L
r
d
LI
L
L
r.
n
a*,
^ /
w
**
«*
k 4
<» K
**
&
**
4*.
,*' v
o'
2-39
REOTRICTEB
REF ID: A5 68 95
Table l6-C . — The 53 digraphs from Table 6- A -which comprise 50$ of
the total, arranged according to frequencies reduced to a "base of 5/000
digraphs, shown with the corresponding frequencies of the same digraphs
from Table l6-B (also reduced to a base of 5/000) .1
Dig,
6-A
16-B
Dig,
6— A
16-B
EN
111
79
FO
4o
54
RE
98
94
FI
39
35
ER
87
86
RA
39
28
NT
82
33
ET
37
34
TH
• 78
55
LE
37
31
ON
77
84
OU
37
39
nr
75
65
MA
36
55
TE
71
36
TW
36
31
AN
64
4l
EA
35
28
OR
64
44
IS
35
28
ST
6 3
36
SI
34
34
ED
60
45
DE
33
29,
NE
57
69
HI
33
20 1
VE
57
46
AL
32
21 1
ES
54
44
CE
32
24
ND
52
31
DA
32
4l
TO
50
43
EC
32
36
SE
49
37
RS
31
25
AT
47
37
UR
31
42
TI
45
29
HI
30
24
AR
44
6l
RI
30
191
EE
42
64
EL
29
19 1
RT
.42
24
HT
28
29,
AS
4i
57
LA
28
18 1
CO
4i
39,
RO
28
59
10
4i
TA
28
26
TY
4i
5 1
With the exception of AL, EL, HI, 10, LA, RI, TY, the digraphs of
this table are all from among the 65 digraphs from Table 16-B which
comprise 50$ of the total.
P-4o
ifr EDTRICTED
REF ID: A5 68 95
APPENDICES
\
&
A
A
&
£
A
A 7T.
jtt "
JSl 4 ,_ *
jf
A
m '
*
A-
A
A
A
A
Jilt
A
A
REF ID : A56895
RESTRICTED
APPENDIX 3
WORD AND PATTERN LISTS - ENGLISH i
I'
Section Pages
A. List of words used in military text arranged alphabeti-
cally according to word length 2-10
B» List of words used in military text arranged in rhyming
order according to word length 11-19
C . List of words used in military text arranged alphabeti-
cally according to word pattern, 20-37
D* Digraphic idiomorphs: general 38-39
E. Digraphic idiomorphs: Playfair.... 40-42
F. Digraphic idiomorphs: four-square........ 43-4-5
RESTRICTED
KEF ID : A56895 -
RESTRICTED :
A. LIST OF WORDS USED IN MILITARY TEXT ARRANGED ALPHABETICALLY
ACCORDING TO WORD LENGTH
AM
BY
EM
TWO LETTER WORDS
IN. •
MM
OK
TO
AN
CO
GO
IS
MP ’
ON
US
AS
CP
HE
IT
MY
OR
WD
AT
CQ
HQ
MC
NO
• QM
WE
BE
DO
IF
; ME
OF
SO
WO
BN
ACT
BID
DUN
THREE LETTER WORDS
HAS MIX
PVT
TEN
ADD
BIG
EAT
HER
NAN
QMC
THE
ADJ
BOX
END
HIM
NET
RED
TIN
AGE
BUT
EYE
HIS
NEW
RID 1
' TON
AGO
BUY
FAR
HOW
NOT
ROB
TOO
AID
CAM
FEW
ILL
NOW
RUN
TOP
AIM '
CAN
FIT
ITS
OFF
SAW
TRY
AIR
CAR
FIX
JIG
OLD
SAY
TUB
ALL
CAV
FOR
JOB
ONE
SEA
TWO
AND
COL
FOX
KEG
OUR
SEE
USE
ANY
CPL
GAL
LAW
OUT
SET
VAT
APT
CUT
GAS
LAY
OWE
SGT
WAR
ARC
CWT
GEN
LET
OWN
SHE
WAS
ARE
DAY
. GET
LOT
PAR
SIX
WAY
ARM
DID
GHQ
LOW
PAY
SPY
WET
ASK
DIE
GOT
MAJ
PEN
SUM
WGT
BAD
DOG
GUN
MAN
PER
SUN
WON
BAG
DRY
HAD
MAT
PIN
TAN
YET
BAR
DUE
HAM
MEN-
PUT
TAX
YOU
ABLE
BOTH
EACH
FOUR LETTER WORDS
FLEE
HIGH
LATE .
MAIN
AIDE
. BULB
EAST
FORM
HILL
LEAD
MANY
ALLY
BULK
EASY
FOUR
HITS
LEAK
MASK
ALSO
CALL
EDGE
FROM
HOLD
LEFT
MASS
AREA
CELL
EYES
FULL
HOOK
LESS
MEAT
ARMY
CITY
FALL
FUSE
INTO
LIEU
MEET
ASIA
CODE
FARM
FUZE
ITEM
LINE
MESS
AWAY
COOK
FAST
GUNS
JOIN
LIST
MIKE
AXIS
DARK
FEEL
HALF
JULY
LOAD
MILE
BACK
DASH
FEET
HALT
JUNE
LONG
MINE
BASE
DATE
FELL
HAND
JUST
LOOK
MORE
BEEN
DAYS .
FILE
HARD
KEEP
LOSS
MOVE
BLUE
DIRT
FIRE
HAVE
KIND
LOST
MTCL
BODY
DOWN
FIRM
HEAD
KING
LOVE
MULE'
BOMB
DRAW
FIVE
HERD
LAND
MADE
NAVY
BOOK
DUMP
FLAG
HERE
LAST
MAIM
NEAR
RESTRICTED'
3-2
REF ID: A5 68 95
RESTRICTED
1 ,
FOUR LETTER WORDS— Continued
NEXT
PARK
REAR
SHOT
TEAM
TOOK
WEST
NINE
PASS
RIOT
SIDE
TENT
TOOL
WHAT
NOON
PIPE *
ROAD
SOME
TEXT
TOWN
WHEN -
NOTE
PLAN
ROUT
SOON
THAN
TYPE
WILL
OBOE
POST
RULE
STOP
THAT
UNIT
WIRE
OMIT
PUMP
RUSH
SUNK
THEM
VARY
WITH
ONCE
PUSH
SAID
TAKE
THEN
•VERY
XRAY
ONLY
RAID
SAME
TALK
THEY
WEAK
YOKE
OPEN
RAIL
SANK
TANK
THIS
WEEK
ZERO
ORAL
RAIN
SEEN
TARE
TIME
WELL
ZONE
OVER
RANK
SHIP
TASK
TONS
WERE
!
FIVE LETTER WORDS
ABOUT
BOATS
DECKS
FIGHT
LATER
PRIOR
SHIPS
TITLE
AFTER
BOMBS
DEFER
FIRES
l^EAST
PROOF
SHORE
TODAY
AGAIN
BOOTH
DELAY
FIRST
LEAVE
. PROVE
SIEGE
TOTAL
AGENT
BREAK
DEPOT
FLANK
LEVEL
QUEEN
SIGHT
TRACT
ALARM
BRIBE
DEPTH
FLARE
LIGHT
QUICK
SIXTH
TRAIN
ALERT
BROKE
DOCKS
FLATS
LIMIT
QUIET
SIXTY
TROOP
ALIGN
BURST
DRAWN
FLEET
LOCAL
RADIO
SLOPE
TRUCE
ALINE
CANAL
DRESS
FOGGY
MAJOR
RAFTS
SMALL
TRUCK
ALLOW
CASES
DRILL
FORCE
MARCH
RAIDS
SMOKE
UNDER
ALONG
CAUSE
DRIVE
FORTY
METER
RALLY
SOUTH
UNION
AMONG
CEASE
EAGER •
FRESH
MILES
RANGE
SPEED
UNITS
ANNEX
CHECK
EARLY
FRONT
MOTOR
RAPID
SPELL
USUAL
APPLY
CHIEF
EIGHT
GATES
NAVAL
REACH
SPLIT
VALOR
APRIL
CLEAR
ENEMY
GAUGE'
NIGHT
READY
SQUAD
VISIT
AREAS
CLERK
ENTER
GIVEN
NINTH
REFER
STAFF
' VITAL
ARMOR
CLOSE
EQUAL
GOING
NORTH
REPEL
STAKE
VOCAL
ASSET
COAST
EQUIP
GROUP
ORDER
RIDGE
START
VOICE
AWAIT
COLON
ERASE
GUARD
OTHER
RIGHT
x STEEL
WAGON
AWARD
COMMA
ERROR
GUEST
PACKS
RIGID
SUGAR
WEIGH
BAKER
CORPS
ETHER
HEAVY
PAIRS
RIVER
TAKEN
WHEEL
BANKS
COUNT
EVERY
HONOR
PARTY
ROGER
TANKS
WHERE
BARGE
COVER
FATAL
HORSE
PETER
ROUTE
TENTH
WHICH
BEACH
CREEK
FEARS
HOURS
PLACE
SCALE
THEIR
WIDTH
BEGIN
CREST
FERRY
HOUSE
PLAIN
SEIZE
THERE
WIPED
BEING
CROSS
FIELD
ISSUE
PLANS
SEVEN
THESE
WOODS
BLACK
CURVE
FIFTH
JAPAN
POINT
SHELL
THIRD
YARDS
BLIND
DAILY
FIFTY
LARGE
PRESS
SHIFT
THREE
ZEBRA
o
REDTRICTEPr
REF ID : A56895
RES¥niC ¥E D
SIX LETTER WORDS
ACCEPT
BOMBED
DEGREE
FIERCE
LESSON
OTHERS
• RESUME
SUFFER
ACCESS
BOMBER
DEPART
FILING
LETTER
Output
RETIRE
SUMMER
ACROSS
BOTTOM
DEPEND
FINISH
LINING
panama
RETURN
SUMMIT
ACTION
BRANCH
DEPLOY
FIRING
LIQUID
PARADE
REVIEW
SUMMON
ACTIVE
BREACH
DESERT
FLIGHT
LITTER
PARLEY
RIDING
SUNDAY
ADJUST
BREEZE
DETACH
FLYING
LITTLE
PASSED
ROCKET
SUNKEN
ADVICE
BRIDGE
DETAIL
FOLLOW
LOCATE
PASSES
ROUTED
SUNSET
ADVISE
BROKEN
DEVICE
FORCES
LOSSES
PATROL
ROUTES
SUPPLY
AFFAIR
BUREAU
DEVISE
FORMAL
MANAGE
PERIOD
RUBBER
SURVEY
ALASKA
CANADA
DIRECT
FORMED
MANNER
PICKET
RUNNER
SWITCH
ALLEGE
CANCEL
DIVERT
FOUGHT
MANUAL
PINCER
SALARY
SYSTEM
ALLIED
CANNOT
DIVIDE
FOURTH
MEAGER
PISTOL
SCHEME
TABLES
ALLIES
CANVAS
DOCTOR
FRIDAY
MEDIUM
PLACES
SCHOOL
TANKER
ALWAYS
CASUAL
DOLLAR
FUTURE
MEMBER
PLANES
SCORED
TARGET
ANIMAL
CAUSED
DOWNED
GARAGE
METHOD
POINTS
SCREEN
TATTOO
ANNUAL
CENTER
DRYRUN
GEORGE
METRIC
POISON
SEAMAN
TERROR
ANYWAY
CHANGE
DUGOUT
GREASE
MINING
POLICE
SEAMEN
THIRTY
APPEAR
CHARGE
DURING
GROUND
MINUTE
PONTON
SEARCH
THOUGH
ARABIA
CHEESE
EFFECT
GUNNER
MIRROR
POSTAL
SECOND
T! !REAT
ARMIES
CHURCH
EFFORT
HALTED
MOBILE
PREFER
SECTOR
TRAINS
ARMORY
CIPHER
EIGHTH
HAMMER
• MONDAY
PROMPT
SECURE
TRENCH
ARREST
. CIRCLE
EIGHTY
HAPPEN
MORALE
PROPER
SELECT
TROOPS
ARRIVE
COFFEE
EITHER
HARBOR
MORTAR
PURSUE
SERIAL
TURRET
ASSETS
COLORS
ELEVEN
HELPER
MOVING
RADIAL
SETTLE
TWELVE
ASSIST
COLUMN
EMBARK
HIGHER
MURDER
RAIDED
SEVERE
TWENTY
ASSURE
COMBAT
EMPLOY
HOURLY
MUZZLE
RATION
SHELLS
UNABLE
ATTACH
COMMIT
ENCODE
INDEED
NAUGHT
RAVINE
SIGCOM
UNITED
ATTACK
COMMON
ENGAGE
INFORM
NEARER
RECORD
SIGNAL
UNLESS
ATTAIN
CONVEY
ENGINE
INLAND
NINETY
REDUCE
SINGLE
VALLEY
AUGUST
CONVOY
ENROLL
INTEND
NORMAL
REFILL
SLIGHT
VERBAL
BANNER
COURSE
ENTIRE
INTENT
NOTING
REFUGE
SPHERE
VERIFY
BARBED
CREDIT
ERASER
INVENT
NOUGHT
REFUSE
SPOOLS
VESSEL
BARGES
CRISIS
ESCORT
ISLAND
NOVICE
REJECT
SPOONS
VICTIM
BATTEN
CRITIC
EUROPE
ISSUES
NOZZLE
RELIEF
STATES
VICTOR
BATTLE
DAMAGE
EXCEPT
KEEPER
NUMBER
REMAIN
STATUS
VISITS
BEETLE
DEBARK
EXCESS
KILLED
OCCUPY
REMEDY
STRAFE
VISUAL
BEFORE
DECIDE
EXCITE
LADDER
OFFEND
REPAIR
STREET
WEIGHT
BETTER
DECODE
EXPECT
LANDED
OFFICE
REPORT
STRESS
WIRING
BEYOND
DECREE
EXPELS
LAUNCH
OPPOSE
RESCUE
STRIPS
WITHIN
BILLET
DEFEAT
EXPEND
LEADER
ORDERS
RESIST
SUBMIT
WOODED
BITTER
DEFECT
EXTEND
LEAGUE
ORIENT
RESULT
SUDDEN
ZIGZAC-
BODIES
DEFEND
EXTENT
SEVEN LETTER WORDS
ABANDON
ALMANAC
APPOINT
ASIATIC
AVIATOR
BATTERY
BETWEEN
ABSENCE
AMMETER
APPROVE
ASSAULT
AWKWARD
BATTLES
BICYCLE
ADDRESS
ANALYZE
ARMORED
ATTACKS
BAGGAGE
BEARING
BINDING
ADVANCE
ANOTHER
ARRANGE
ATTEMPT
BALLOON
BECAUSE
BIVOUAC
AGAINST
ANTENNA
ARRIVAL
AVERAGE
BARRAGE
BEDDING
BOMBARD
3- 1 !'
RESTRICTED
REF ID: A5 68 95
SEVEN LETTER WORDS— Continued
BOMBERS
DEBOUCH
FITTING
LANDING
PACKAGE
REQUEST
SUPPOSE
BOMBING
DECIDED
FOGHORN
LEADING
PASSAGE
REQUIRE
SURPLUS
BOYCOTT
DECLARE
FORCING
LECTURE
PASSIVE
RESERVE
SUSPEND
BRIBERY
DECODED
FORGING
LIAISON
' PATROLS
RESPECT
TACTICS
BRIGADE
DEFENSE
FORWARD
LIBRARY
PAYR'OLL
RESPOND
TALKING
CALIBER
DELAYED
FOXHOLE
LICENSE
PLACING
RETIRED
TARGETS
CALIBRE
DELIVER
FUELOIL
LIFTING
PLATO&N
RETREAT
TERRAIN
CAPTAIN
DERRICK
FURNISH
Lb At) TNG
POUNDER
REVENUE
THATTHE
CAPTIVE
DESTROY
FURTHER
LOGICAL
PRAIRIE
REVERSE
THROUGH
CARRIER
DETRAIN
GASSING
LOOKOUT
PRECEDE
REVOLVE
TOBACCO
CAVALRY
DETRUCK
GENERAL
MACHINE
PREPARE
ROUTINE
TONIGHT
CENTRAL
DEVELOP
GETTING
MANDATE
PRESENT
RUNNING
TONNAGE
CHANGES
DIAGRAM
GLASSES
MANNING
PRESSED
SAILORS
TORPEDO
CHANNEL
DISCUSS
GRADUAL
MAPPING
PRIMARY
SATISFY
TRACTOR
CHARLIE
DISEASE
GRENADE
MARCHED
PROCEED
SECRECY
TRAFFIC
CHASSIS
DISMISS
GUARDED
MARSHAL
PROGRAM
SECTION
TRAWLER
CIRCUIT
DISTILL
HALTING
MARTIAL
PROMOTE
SECTORS
TRIGGER
CLIPPER
DROPPED
HASBEEN
MAXIMUM
PROPOSE
SERVICE
TUESDAY
COASTAL
EASTERN
HEADING
MEDICAL
PROTECT
SESSION
TWELFTH
COLLECT
ECHELON
HEAVIER
MESSAGE
PROTEST
SETBACK
UNKNOWN
COLLEGE
ELEMENT
HIGHEST
MESSING
PROVOST
SEVENTH
UNUSUAL
COLQNEL
ELEVATE
HOLDING
MILITIA
PURPOSE
SEVENTY
USELESS
COMMAND
EMBASSY
HORIZON
MINIMUM
PURSUIT
SEVERAL
UTILITY
COMMEND
ENCODED
HOSTILE
MISFIRE
PUSHING
SHELLED
VACANCY
COMMENT
ENEMIES
HUNDRED
MISSING
QUARTER
SHORTLY
VARYING
COMMUTE
ENFORCE
ICEBERG
MISSION
QUICKLY
SIGNIFY
VESSELS
COMPANY
ENGAGED
ILLEGAL
MORNING
RADIATE
SIMILAR
VICTORY
COMPASS
ENTENTE
ILLNESS
NATURAL
' RAIDING
SIMPLEX
VILLAGE
CONCEAL
ENTRAIN
INCLUDE
NEAREST
RAILWAY
SINKING
VISIBLE
CONDEMN
ENTRUCK
INFLICT
NIGHTLY
RAINING
SIXTEEN
VISITOR
CONDUCT
ENVELOP
INITIAL
NOTHING
RAPIDLY
SLOPING
WARFARE
CONFINE
EXCLUDE
INQUIRE
NUMBERS
REACHED
SMOKING
WARSHIP
CONTACT
EXPLAIN
INQUIRY
OBSERVE
RECEIPT
SOLDIER
WEATHER
CONTAIN
EXPRESS
INSPIRE
OCTOBER
RECEIVE
STARTER
WESTERN
CONTROL
EXTRACT
INSTALL
OFFENSE
RECOVER
STATION
WHETHER
CORRECT
EXTREME
INSTANT
OFFICER
RECRUIT
STEAMER
WILLIAM
COUNCIL
FALLING
INVADED
OMITTED
REDUCED
STOPPED
WINDAGE
COURIER
FARTHER
ISLANDS
OPERATE
REFUGEE
STORAGE
WITHOUT
COVERED
FEDERAL
ISSUING
OPINION
REGULAR
SUCCESS
WITHTHE
CROSSED
FIFTEEN
JANUARY
ORDERED
RELEASE
SUGGEST
WITNESS
CRUISER
FIGHTER
JUMPOFF
OUTPOST
RELIEVE
SUMMARY
WOUNDED
CURRENT!
FILLING
KITCHEN
OUTSIDE
REPAIRS
SUNRISE
WRECKED
CYCLONE
FINDING
KILLING
PACIFIC
REPLACE
SUPPORT
WRITTEN
DAMAGED;
FISHING
EIGHT
LETTER WORDS
ACTIVITY
• ADVANCED
AIRBORNE
AIRPLANE
ANNOUNCE
APPROACH
ASSEMBLE
ACTUALLY
ADVANCES
AIRCRAFT
ALTITUDE
ANTITANK
APPROVAL
ASSEMBLY
ADJACENT
ADVISING
AIRDROME
AMERICAN
APPARENT
ARMAMENT
ASSIGNED
ADJUTANT
ADVISORY
AIRFIELD
ANALYSIS
APPEARED
ARRESTED
ASSOONAS
• - j'iflDTniCTEU
3-5
RESTRICTED
REF ID: A56895
EIGHT LETTER WORDS — Continued
ATLANTIC
CRITIQUE
DRIFTING
FORENOON
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REF ID : A56895
- HEaTHICTED .
NINE LETTER WORDS
ACCESSORY
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ADMISSION
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AEROPLANE
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3-7
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REF ID : A56895
SUBMITTED
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NINE LETTER WORDS— Continued
SUSPENDED TELEPHONE THEREFORE UNTENABLE
WEDNESDAY
SUSPICION TENTATIVE TRANSPORT VARIATION
WITNESSES
TECHNICAL TERRITORY TWENTIETH WATERTANK
YESTERDAY
TECHNIQUE
TEN LETTER WORDS
COLLISIONS
DESPATCHES
EXPENDABLE
MAINTAINED
COMMANDANT
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MACHINEGUN
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REF ID: A5 68 95
- REaTRICTCD ■
TEN LETTER WORDS— Continued
REVOLUTION SUBMISSION SUSPENSION TRANSPORTS UNEXPENDED
SANITATION SUBSTITUTE SUSPICIONS TRANSVERSE UNSUITABLE
SEPARATION SUCCESSFUL SUSPICIOUS TROOPSHIPS VICTORIOUS
SIGNALLING SUCCESSIVE ' THIRTEENTH TWENTY FIVE VISIBILITY
SIMILARITY SUFFICIENT THREATENED UNDERSTAND WILLATTACK
STATISTICS SUPPORTING TRAJECTORY UNDERSTOOD WITHDRAWAL
SUBMARINES
ELEVEN LETTER WORDS
ACCESSORIES CONCENTRATE EMPLACEMENT IWTERfcERPTS REAPPOINTED
AERONAUTICS CONFINEMENT ENCOUNTERED INTERESTING RECOGNITION
ALTERNATING CONSTITUTED ENEMYPLANES INTERFERING RECOMMENDED
APPLICATION CONSUMPTION ENFORCEMENT INTERPRETER RECONNOITER
APPOINTMENT CONTINENTAL ENGAGEMENTS INTERRUPTED REPLACEMENT
APPROACHING CONTROVERSY ENGINEERING INTERVENING REQUIREMENT
APPROPRIATE COOPERATION ESTABLISHED INVESTIGATE REQUISITION
APPROXIMATE CORPORATION ESTIMATEDAT LEGISLATION RESERVATION
ARBITRATION CORRECTNESS EXAMINATION * LIGHTBOMBER RESIGNATION
ARMOREDCARS CREDENTIALS EXPLANATION MAINTENANCE RESPONSIBLE
ARRANGEMENT CUSTOMHOUSE EXTENSIVELY MANUFACTURE RESTRICTION
ASSESSMENTS DEBARKATION EXTERMINATE ' MEASUREMENT RETALIATION
ASSIGNMENTS DEMONSTRATE FINGERPRINT | NATIONALISM RETROACTIVE
ASSOCIATION DESCRIPTION FIRECONTROL 1 NATIONALITY SCHOOLHOUSE
BATTLEFIELD DESCRIPTIVE HEAVYBOMBER - NAVALATTACK SEVENTEENTH
BATTLESHIPS DESIGNATION HEAVYLOSSES 1 NAVALBATTLE SEVENTYFIVE
BELLIGERENT DESTRUCTION HOSTILITIES NAVALFORCES SIGNIFICANT
BLOCKBUSTER DETERIORATE IMMEDIATELY NECESSITATE SMOKESCREEN
BOMBARDMENT DEVELOPMENT IMMIGRATION OBSERVATION STRATEGICAL
CATASTROPHE DISAPPEARED " IMPEDIMENTA OVERWHELMED SUBSISTENCE
CERTIFICATE DISCONTINUE IMPROVEMENT PARENTHESIS SUITABILITY
CIRCULATION DISCREPANCY INCOMPETENT PARENTHESES SUPERIORITY
COEFFICIENT DISINFECTED INDEPENDENT . PENETRATION SURRENDERED
COINCIDENCE DISPOSITION INFLAMMABLE PERFORMANCE SYNCHRONIZE
COMMUNICATE DISTINCTION INFORMATION PHILIPPINES TEMPERATURE
COMMUNIQUES DISTINGUISH INSPIRATION PHOTOGRAPHY THERMOMETER
COMPARTMENT DYNAMOMETER INSTITUTION PREARRANGED TOPOGRAPHIC
COMPETITION ECHELONMENT INSTRUCTION PREPARATION TRADITIONAL
COMPOSITION EFFECTIVELY INSTRUMENTS PRELIMINARY TRANSFERRED
COMPUTATION ELECTRICITY ' INTELLIGENT PROGRESSIVE WITHDRAWING
CONCEALMENT EMBARKATION INTERCEPTED RANGEFINDER
TWELVE LETTER WORDS
ADVANTAGEOUS CARELESSNESS CONCENTRATED CONSIDERABLE COORDINATION
AGRICULTURAL COMMENCEMENT CONCILIATION CONSTITUTING DECENTRALIZE
ANNOUNCEMENT COMMENDATION CONFIDENTIAL CONSTITUTION DECIPHERMENT
ANTIAIRCRAFT COMMISSIONED CONFIRMATION CONSTRUCTION DEMONSTRATED
ANTICIPATION COMMISSIONER CONFISCATION CONTINUATION DEPARTMENTAL
BREAKTHROUGH COMPENSATION CONFORMATION CONVALESCENT DIFFICULTIES
CANCELLATION COMPLETENESS CONSCRIPTION CONVERSATION DISORGANIZED
3-9
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REF ID: A5 68 95
DISPLACEMENT
DISSEMINATED
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ENTANGLEMENT
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FIGHTERPLANE
GENERALALARM
GENERALSTAFF
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TWELVE LETTER WORDS— Continued
HYDROGRAPHIC
ILLUMINATING
ILLUMINATION
ILLUSTRATION
INAUGURATION
INCOMPETENCE
INEFFICIENCY
INSTRUCTIONS
INTELLIGENCE
INTERDICTION
INTERFERENCE
INTERMEDIATE
INTERRUPTION
INTERVENTION
INTRODUCTION
INTRODUCTORY.
IRREGULARITY.'
LIGHTBOMBERS
MARKSMANSHIP
MEASUREMENTS
MEDIUMBOMBER
MOBILIZATION
NONCOMBATANT
NORTHWESTERN
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PREPARATIONS
PREPAREDNESS
PRESERVATION
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PROCLAMATION
psychromeTer
RADIOSTATION
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RESPECTFULLY
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SATISFACTORY
SEARCHLIGHTS
SHARPSHOOTER
THIRTEEN LETTER WORDS
CORRESPONDING
COUNTERATTACK
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DEMONSTRATION
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INTERNATIONAL
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MEDIUMBOMBERS
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FOURTEEN LETTER WORDS
DEMOBILIZATION
DISCONTINUANCE
DISTINGUISHING
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INTERPRETATION
INVESTIGATIONS
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METEOROLOGICAL
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RECOMMENDATION
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■R ESTRICTED
REF ID: A5 68 95
TtESTIUCTED
B. LIST OF WORDS USED IN MILITARY TEXT ARRANGED IN RHYMING ORDER
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REF ID : A56895
FIVE LETTER WORDS
COMMA
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TITLE
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REF ID: A56895
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REF ID: A5 68 95
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SUFFICIENT
IMPOSSIBLE
CONNECTING
RECREATION
HYGROMETER
CONVENIENT
ASPOSSIBLE
INFLICTING
IRRIGATION
AMBASSADOR
EQUIVALENT
RECEPTACLE
EXPEDITING
NAVIGATION
INSTRUCTOR
ENGAGEMENT
MOTORCYCLE
RECRUITING
REGULATION '
BALLISTICS
MANAGEMENT
AUTOMOBILE
ATTEMPTING
POPULATION
STATISTICS
EXCITEMENT
DISCIPLINE
SUPPORTING
ESTIMATION
CROSSROADS
DETACHMENT
QUARANTINE
EXTINGUISH
DOMINATION ;
DESPATCHES
ATTACHMENT
ENTERPRISE
NINETEENTH
DETONATION ‘
DISPATCHES
EXPERIMENT
TRANSVERSE
EIGHTEENTH
OCCUPATION ,
ASSEMBLIES
ENROLLMENT
COORDINATE
THIRTEENTH
SEPARATION
FACILITIES
ASSIGNMENT.
ILLUMINATE
FOURTEENTH
DECORATION
ACTIVITIES
ATTAINMENT
ANTICIPATE
WILLATTACK
LIMITATION 1
CASUALTIES
INTERNMENT
ILLITERATE
ARTIFICIAL
SANITATION
FRONTLINES
GOVERNMENT
ILLUSTRATE
CREDENTIAL
INVITATION
SUBMARINES
ASSESSMENT
COMPENSATE
ADDITIONAL
EVACUATION
OBJECTIVES
COMMITMENT
DISTRIBUTE
ACCIDENTAL
EVALUATION
ENEMYTANKS
DEPARTMENT
SUBSTITUTE
REGIMENTAL
EXCAVATION '
SUSPICIONS
ENLISTMENT
CONSTITUTE
INDIVIDUAL
COLLECTION
COLLISIONS
INSTRUMENT
COMMUNIQUE '
WITHDRAWAL
CONNECTION
PROVISIONS
DEPLOYMENT
TWENTYFIVE
AIRCONTROL
* INSPECTION
EXPLOSIONS
EMPLOYMENT
SUCCESSIVE
SUCCESSFUL
CORRECTION
FORMATIONS
PERSISTENT
IMPRESSIVE
RESPECTFUL
PROTECTION’
OPERATIONS
AIRSUPPORT
LOCOMOTIVE
MEMORANDUM
EXHIBITION
DIRECTIONS
CONSPIRACY
CENTRALIZE
SUSPENSION
EXPEDITION
CONDITIONS
DEFICIENCY
NATURALIZE
DISPERSION
DEFINITION
TROOPSHIPS
EFFICIENCY
DEMOBILIZE
CONCESSION
AMMUNITION
NEWSPAPERS
COMPLETELY
COMMANDING
CONFESSION
OPPOSITION '
' KILOMETERS
APPARENTLY
DEBOUCHING
DEPRESSION
PROPORTION
DESTROYERS
INCENDIARY
DETRUCKING
IMPRESSION
REVOLUTION
TRANSPORTS
COMMISSARY
ENTRUCKING
POSSESSION
MACHINEGUN
SUSPICIOUS
ELEMENTARY
ENCIRCLING
SUBMISSION
BATTLESHIP
VICTORIOUS
LABORATORY
SIGNALLING
COMMISSION
CENSORSHIP
CIRCUITOUS
TRAJECTORY
PATROLLING
PERMISSION
ARMOREDCAR
CONTINUOUS
CAPABILITY
OVERCOMING
DISCUSSION
DIVEBOMBER
PHOSPHORUS
AUDIBILITY
DETRAINING
CONCLUSION
COMMANDEER
FLASHLIGHT
VISIBILITY
CONCERNING
DEDICATION
DISPATCHER
COMMANDANT
SIMILARITY
INDICATING
INDICATION
MILLIMETER
LIEUTENANT
INSECURITY
ANTEDATING
-
ELEVEN LETTER WORDS
IMPEDIMENTA
SURRENDERED
CONSTITUTED
INFLAMMABLE
CERTIFICATE
. TOPOGRAPHIC
ENCOUNTERED
BATTLEFIELD
RESPONSIBLE
COMMUNICATE
' RECOMMENDED
TRANSFERRED
PERFORMANCE
NAVALBATTLE
INVESTIGATE
PREARRANGED
DISINFECTED
MAINTENANCE
TEMPERATURE
APPROPRIATE
ESTABLISHED
REAPPOINTED
COINCIDENCE
MANUFACTURE
APPROXIMATE
OVERWHELMED
INTERCEPTED
SUBSISTENCE
schoolhduSe
EXTERMINATE
DISAPPEARED
INTERRUPTED
CATASTROPHE
CUSTOMHOUSE
DETERIORATE
RESTRICTED 3-17
ftjgflTRICTED
REF ID : A568 95
CONCENTRATE
DEMONSTRATE
NECESSITATE
DISCONTINUE
SEVENTYFIVE
PROGRESSIVE
RETROACTIVE
DESCRIPTIVE
SYNCHRONIZE
APPROACHING
INTERVENING
ENGINEERING
INTERFERING
ALTERNATING
INTERESTING
WITHDRAWING
DISTINGUISH
SEVENTEENTH
NAVALATTACK
STRATEGICAL
TRADITIONAL
CONTINENTAL
FIRECONTROL
NATIONALISM
TRANSPACIFIC
HYDROGRAPHIC
UNIDENTIFIED
COMMISSIONED
DISSEMINATED
CONCENTRATED
DEMONSTRATED
DISORGANIZED
SIGNIFICANCE
INTELLIGENCE
INTERFERENCE
INCOMPETENCE
CONSIDERABLE
FIGHTERPLANE
INTERMEDIATE
DECENTRALIZE
GENERALSTAFF
TRANSFERRING
ENTERPRISING
ILLUMINATING
DISTRIBUTING
-nEOTniCTEDT
ELEVEN LETTER WORDS— Continued
SMOKESCREEN
APPLICATION
ASSOCIATION
RETALIATION
DEBARKATION
EMBARKATION
LEGISLATION
CIRCULATION
INFORMATION
EXPLANATION
DESIGNATION
RESIGNATION
EXAMINATION
PREPARATION
' COOPERATION
IMMIGRATION
INSPIRATION
CORPORATION
PENETRATION
ARBITRATION
COMPUTATION
OBSERVATION
RESERVATION
RESTRICTION
DISTINCTION
DESTRUCTION
INSTRUCTION
RECOGNITION
REQUISITION
COMPOSITION
DISPOSITION
COMPETITION
DESCRIPTION
CONSUMPTION
INSTITUTION
LIGHTBOMBER
HEAVYBOMBER
RANGEFINDER
DYNAMOMETER
THERMOMETER
INTERPRETER
RECONNOITER
BLOCKBUSTER
AERONAUTICS
NAVALFORCES
ACCESSORIES
HOSTILITIES
ENEMYPLANES
PHILIPPINES
PARENTHESES
HEAVYLOSSES
COMMUNIQUES
PARENTHESIS
CREDENTIALS
BATTLESHIPS
ARMOREDCARS
CORRECTNESS
ENGAGEMENTS
ASSIGNMENTS
ASSESSMENTS
INSTRUMENTS
INTERCERPTS
ESTIMATEDAT
SIGNIFICANT
INDEPENDENT
INTELLIGENT
COEFFICIENT
BOMBARDMENT
REPLACEMENT
EMPLACEMENT
ENFORCEMENT
ARRANGEMENT
TWELVE LETTER WORDS
CONSTITUTING
BREAKTHROUGH
GEOGRAPHICAL
CONFIDENTIAL
PRESIDENTIAL
RECREATIONAL
AGRICULTURAL
DEPARTMENTAL
UNSUCCESSFUL
GENERALALARM
VETERINARIAN
TRANSMISSION
VERIFICATION
CONFISCATION
COMMENDATION
CONCILIATION
CANCELLATION
PROCLAMATION
CONFIRMATION
CONFORMATION
COORDINATION
ILLUMINATION
ANTICIPATION
REGISTRATION
ILLUSTRATION
INAUGURATION
COMPENSATION
CONVERSATION
RADIOSTATION
CONTINUATION
PRESERVATION
MOBILIZATION
ORGANIZATION
INTERDICTION
ROADJUNCTION
INTRODUCTION
CONSTRUCTION
INTERVENTION
CONSCRIPTION
INTERRUPTION
DISTRIBUTION
SUBSTITUTION
CONSTITUTION
NORTHWESTERN
SOUTHWESTERN
Marksmanship
MEDIUMBOMBER
COMMISSIONER
PSYCHROMETER
SHARPSHOOTER
DIFFICULTIES
UNITEDSTATES
PREPARATIONS
OBSTRUCTIONS
INSTRUCTIONS
LIGHTBOMBERS
HEAVYBOMBERS
HEADQUARTERS
PREPAREDNESS
COMPLETENESS
CARELESSNESS
SEARCHLIGHTS
REPLACEMENTS
3-18
CONFINEMENT
REQUIREMENT
MEASUREMENT
IMPROVEMENT
CONCEALMENT
ECHELONMENT
DEVELOPMENT
APPOINTMENT
COMPARTMENT
BELLIGERENT
INCOMPETENT
FINGERPRINT
DISCREPANCY
PHOTOGRAPHY
IMMEDIATELY
EXTENSIVELY
EFFECTIVELY
PRELIMINARY
CONTROVERSY
ELECTRICITY
NATIONALITY
SUITABILITY
SUPERIORITY
EMPLACEMENTS
MEASUREMENTS
ADVANTAGEOUS
SIMULTANEOUS
ANTIAIRCRAFT
NONCOMBATANT
CONVALESCENT
DISPLACEMENT
COMMENCEMENT
ANNOUNCEMENT
ENTANGLEMENT
DECIPHERMENT
ENCIPHERMENT
REENLISTMENT
INEFFICIENCY
SUCCESSFULLY
RESPECTFULLY
SATISFACTORY
INTRODUCTORY
IRREGULARITY
REF ID : A56895
RESTRICTED
TRANSATLANTIC
DISTINGUISHED
DECENTRALIZED
DISAPPEARANCE
IMPRACTICABLE
INDETERMINATE
CORRESPONDING
CONCENTRATING
COUNTERATTACK
CHARACTERISTIC
RECONNAISSANCE
DISCONTINUANCE
CORRESPONDENCE
ADMINISTRATIVE
REPRESENTATIVE
DISTINGUISHING
RESTRICTED
THIRTEEN LETTER WORDS
CHRONOLOGICAL
CONGRESSIONAL
INTERNATIONAL
SPECIFICATION
QUALIFICATION
COMMUNICATION
ACCOMMODATION
INVESTIGATION
DISSEMINATION
DETERMINATION
EXTERMINATION
CONSIDERATION
CONCENTRATION
DEMONSTRATION
QUARTERMASTER
CIRCUMSTANCES
DISCREPANCIES
PRELIMINARIES
FIGHTERPLANES
INSTALLATIONS
MEDIUMBOMBERS
MISCELLANEOUS
INSTANTANEOUS
REENFORCEMENT
REINFORCEMENT
REIMBURSEMENT
REINSTATEMENT
FOURTEEN LETTER WORDS
RECONNOITERING
METEOROLOGICAL
CIRCUMSTANTIAL
CLASSIFICATION
IDENTIFICATION
RECOMMENDATION
ADMINISTRATION
INTERPRETATION
TRANSPORTATION
CENTRALIZATION
NATURALIZATION
DEMOBILIZATION
I
3-19
ESTABLISHMENT
ENTERTAINMENT
REAPPOINTMENT
WARDEPARTMENT
APPROXIMATELY
EXTRAORDINARY
REVOLUTIONARY
DEPENDABILITY
REORGANIZATION ' -
RECONSTRUCTION
IRREGULARITIES
INVESTIGATIONS
SATISFACTORILY
RESPONSIBILITY
RESTRICTED
REF ID: A56895
C. LIST OF WORDS USED IN MILITARY TEXT ARRANGED ALPHABETICALLY
ACCORDING TO WORD PATTERN
PATTERN AA
A
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9
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3-20
REF ID: A5 68 95
JREOTJRICTE B
PATTERN AA— Continued
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SUBMI
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MISCELLANEOUS PATTERNS
AABA
AGR EEME NT
AABCB
SU FFICI ENT
AABA
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AABCB
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AABA
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BA TTERIE S
AABCA
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AABCDB A
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AABCA
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CA RRIER
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CO MMANDAN T
AABCA
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AABCA
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AABCDEB
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*
/
. REF ID: A5 68 95
RESTRICTED
MISCELLANEOUS PATTERNS— Continued
AABCDEB
A
SSEMBLE
ABA
INVA
DED
AABCDEBC
TR
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ABA
LAN
DED
AABCDEC
CO
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ABA
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AABCDECB
BA
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ABA
WOUN
DED
AABCDED
CO
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AABCDEFA
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ABA
CR
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AABCDEFB
0
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ABA
F
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AABCDEFBA
A
SSEMBLIES
. ABA
D
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AABCDEFC
A
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ABA
D
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AABCDEFC
C
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ABA
D
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AABCDEFD
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ABA
SI
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AABCDEFD
A
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ABA
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AABCDEFDGA
A
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ABA
S
ELE
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AABCDEFGA •
C
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ABA
T
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AABCDEFGABF
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EENLISTMENT
ABA
ELE
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AABCDEFGD
BA
TTLESHIPS
ABA
SCH
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AABCDEFGDAE
C
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ABA
R
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AABCDEFGDE
A
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ABA
DISPLAC
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ABA
AGA IN
ABA
PLAC
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ABA
AGA INST
ABA
ENE
MY
ABA
C
ALA MITY
ABA
G
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RAL
ABA
ALA RM
ABA
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D
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C
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ANA LYZE
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ABA
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ABA
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D
ABA
P
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ABA
COV
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D '
ABA
P
ARA DE
ABA
TH
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ABA
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ABA
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ABA
F
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D
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N
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ABA
P
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ABA
D
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AWA RD
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S
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N
ABA
AWA Y
ABA
S
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NTH
ABA
PRO
BAB LE
ABA
S
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ABA
PRO
BAB LY
ABA
S
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CYC LE
ABA
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CYC LONE
ABA
EYE
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BLOCKA
DED
ABA
FIF
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ABA
GROUN
DED
ABA
FIF
TY
ABA
GUAR
DED
ABA
EIG
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REDTRICTE B 3-22
REF ID: A56895
M ISCELL ANEOUS PATTERNS— Continued
ABA
L IAI SON
ABA
CA RTR IDGE
ABA
PROH IBI T '
ABA '
D RYR UN
ABA
SERV, ICI NG
ABA
DI SAS TER
ABA
RA IDI NG
ABA
CA SES
ABA
R IDI NG
ABA
RE SIS T
ABA
R IGI D
ABA
' SUS PEND
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F ILI NG
ABA
SYS TEM
ABA
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ABA
S TAT ION
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MOB ILI ZE
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DIC TAT OR
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ABA
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ABA
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ABA
TOT ALING
ABA
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ABA
A UGU ST
ABA
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ABA
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ABA
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ABA
SUR VIV ED
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ABAA
*' HAV EBEE N
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ABAA "•
SESS ION
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POS ITI VE
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ABAB
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DOMI NAN CE
ABAB
■ ' TRA ININ G'
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ORD NAN CE
ABAB
CR ISIS
ABA
DOMI NAN T
ABAB
*■ * WI THTH E
ABA
NIN E
ABAB
PAR TITI ON
ABA
NIN ETY
ABACA
C ANADA
ABA
MOR NIN G
ABACA
P ANAMA
ABA
NIN TH
ABACA
PR ECEDE
ABA
OBO E
ABACA
ELEME NT
ABA
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ABACA
ELEME NTARY
ABA
SEMIC OLO N
ABACA
ELEVE N
ABA
c olo'rs
ABACA "
C EMETE RY
ABA
AUT OMO BILE
ABACA
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ABA
PR OMO TE
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AUD IBILI TY
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EXH IBITI ON
ABA
VIG ORO US
ABACA
V ICINI TY
ABA
M OTO R
ABACA
M ILITI A
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ABACA
FAC ILITI ES
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PR OVO ST
ABACA
D IMINI SH
ABA
PIP E
' ABACA
L IMITI NG
ABA
POP ULATED
ABACA
INITI AL
ABA
LIB RAR Y
ABACA
DEF INITI ON
ABA
AI RDR OME
ABACA
D IRIGI BLE
3-23
it- EgTIKCTED
REF ID : A56895
MISCELLANEOUS PATTERNS— Continued
ABACA
SEM IRIGI D
ABACDA
R
ABACA
REQU ISITI ON
ABACDA
U
ABACA
C IVILI AN
ABACDA 1 ' 1
PR
ABACA
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ABACDB
A
ABACADBA
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ABACADC
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TH
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REF ID : A56895
RESTRICTED
MISCELLANEOUS
9
AQAtlDEFA
EXERCISE
ABACDEFAF 1,
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ABACDEFB
DEDICATE
ABACDEFB
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ABACDEFC
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ABACDEFCDFE
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ILLI NG
ABBA
SW
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PATTERNS— Continued
ABBA
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REF ID : A56895
RESTRICTED
MISCELLANEOUS PATTERNS— Continued
ABBCDA
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RESTRICTED - 3.26
REF ID: A5 68 95
I?ESTI*
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MISCELLANEOUS
PATTERNS-
-Continued
ABCA
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ABCA
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ABCA
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ABCA
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m?crroTf<rrprt
3-27
REE ID: A56895
RESTRICTED
MISCELLANEOUS PATTERNS— Continued
ABCA
S
TRAT EGY
ABCAC
P
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ABCA
D
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ABCAC
PRO
TESTS
ABCA
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N
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ABCADCEFGED
l
CONCENTRATE
RESTRICTE D
O
J
23
REF ID : A56895
REPTniCTED
MISCELLANEOUS PATTERNS— Continued
ABCADCEFGEHC
CONCENTRATIN G
ABCADEFA
ENVELOPE
ABCADCEFGEHBC
CONCENTRATION
ABCADEFA
EXPEDITE
ABCADD
D EPRESS ION
ABCADEFA
EXPERIME NT
ABCADD
EXCESS 1
ABCADEFAB
INDICATIN G
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D ISTILL
ABCADEFAB
D ISTINGUIS H
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P OSTOFF ICE j
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INDICATION
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ABCADEFBA
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ABCADDECCFA
UNSUCCESSFU L
ABCADEFC
BOMBARDM ENT
ABCADDEFA
EXCESSIVE
ABCADEFC
CIRCULAR
ABCADEA
ADVANTA GE
ABCADEFC
• U NTENABLE
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ADVANTA GEOUS
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RETROACTIVE
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D ECREASE
ABCADEFD
ADVANCIN G
ABCADEA
S EPTEMBE R
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EXTENDIN G
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R EQUESTE D
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D ISCIPLI NE
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CO NTINGENT
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EXPEDITI NG
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EXPEDITI ON
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EXTENDED
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G ONIOMETE R
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C OMPOSITIO N
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ABCADEFGA
EXPENSIVE
ABCADEB
R ESPECTS
ABCADEFGA
EXTENSIVE
ABCADEB
INCIDEN T
ABCADEFGAF
ECHELONMEN T
ABCADEB
M ISFIRES
ABCADEFGB
C ASUALTIES
Abcadebce
INCIDENCE
ABCADEFGB
CIRCULATI ON
ABCADEC
M ANDATED
ABCADEFGBC
CONCLUSION
ABCADEC
S ECRETAR Y
ABCADEFGC
INDICATED
ABCADEC
GYR OSCOPIC
ABCADEFGC
S TRATEGICA L
ABCADECA
REARGUAR D
ABCADEFGD
EXTENSION
ABCADECAFD
D ISTINCTION
ABCADEFGDC
CONCEALMEN T
ABCADECFC
CONCERNIN G
ABCADEFGE
REPRISALS
ABCADEDA
CO NFINEMEN T
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BOMBARDED
ABCADEDAFB
INVITATION
ABCADEFGHAB
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ABCADEDBD
SUBSTITUT E
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EXTERMINATE
ABCADEDBDE
SUBSTITUTI ON
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EXTERMINATION
ABCADEDC
LI EUTENANT
ABCADEFGHEIGCF
REORGANIZATION
ABCADEDFGA
ENTERPRISE
ABCADEFGHH
R ESPECTFULL Y
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CONCILIATION
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ENTERPRISIN G
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ABCADEEBFGHC
CANCELLATION
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ABCADEED
CANCELLE D
ABCBA
COMP LETEL Y
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CONCESSION
ABCBA
AWKWA RD
ABCADEEFGD
P ROGRESSIVE
ABCBA
CAPAC ITY
ABCADEFA
ECHELONE D
ABCBA
PA CIFIC
REQTmqTED
REF ID : A56895
RESTRICTED
MISCELLANEOUS PATTERNS— Continued
ABCBA
SPE CIFIC
ABCBDEBA
RECEIVER
ABCBA
HIN DERED
ABCBDEBA
REPEATER
ABCBA
DIVID E
ABCBbEFA
REJECTOR
ABCBA
GARAG E
ABCBDEFA
STATIONS
ABCBA
C ITATI ON
ABCBDEFBA
DEVELOPED
ABCBA
LEVEL
ABCBDEFGA
R ESISTANCE
ABCBA '
P REFER
ABCBDEFGBA
DETERMINED .
ABCBA {
REFER
ABCBDEFGHFA
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ABCCA |
LITTL E
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TAXAT ION
ABCCA j
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ABCBA
HOS TILIT Y
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ABCBA
U TILIT Y
ABCCABDEC
C ROSSROADS
ABCBA
AC TIVIT Y
ABCCBADED
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ABCCBCA
BE GINNING
ABCBAAB
P REFERRE D
ABCCBDA
INF LAMMABL E
ABCBAB
DIVIDI NG
ABCCDA
COLLEC T
ABCBAB
AC TIVITI ES
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T RIGGER
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REFERENCE
ABCCDA
RUBBER
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MINIMUM
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ABCBADB
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SUCCESSFU L
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SUCCESSFULL Y
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SUCCESSIVE
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RESEAR CH
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P RESSURE
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STATES
ABCCDAEC
TERRITOR Y
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STATUS
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CORRECTNESS
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STATISTICS
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COMMENCEMEN T
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COMMUNIC ATE
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DESERTED
ABCCDEFA
SUPPLIES
RESTRICTED 3-30
REF ID : A56895
RESTRICTED
M ISCELLANEOUS PATTERNS— Continued
ABCCDEFAGHFBE
COMMUNICATION
ABCDA
INSPI RE
ABCCDEFBGHDGAD
CORRESPONDENCE
ABCDA
LOCAL
ABCCDEFGA
R EAPPOINTE D
ABCDA
LAU
NCHIN G
ABCCDEFGHAFG
R E APPOINTMENT
ABCDA
CO
NDEMN
ABCDA
S ABOTA GE
ABCDA
MACHI
NEGUN
ABCDA
R AILWA Y
ABCDA
NOTIN G
ABCDA
ANIMA L
ABCDA
EXPA
NSION
ABCDA
S ANITA RY
ABCDA
CO
NTAIN
ABCDA
M ARSHA L
ABCDA
MOU
NTAIN
ABCDA
M ARTIA L
ABCDA
I
NTERN AL
ABCDA
E ASTWA RD
ABCDA
FRO
NTLIN E
ABCDA
N ATURA L
ABCDA
I
NTREN CH
ABCDA
N ATURA LIZE
ABCDA
C
ONTRO L
ABCDA
TE CHNIC- AL
ABCDA
H
ORIZO N
ABCDA
COUNC IL
ABCDA
OUTBO ARD
ABCDA
R EACHE D
ABCDA
PROMP T
ABCDA
L EAGUE
ABCDA
RECOR D
ABCDA
EASTE RLY
ABCDA
REPOR T
ABCDA
EASTE RN
ABCDA
RETUR N
ABCDA
W EATHE R
ABCDA
P
RIMAR Y
ABCDA
H EAVIE R
ABCDA
RIVER
ABCDA
INS ECURE
ABCDA
ROGER
ABCDA
S ECURE
ABCDA
FA
RTHER
ABCDA
R EDUCE
ABCDA
FU
RTHER
ABCDA
SCH EDULE
ABCDA,
NO
RTHER LY
ABCDA
B EFORE
ABCDA
SATIS FY
ABCDA
R EFUGE
ABCDA
SHIPS
ABCDA
R EFUSE
ABCDA
WAR
SHIPS
ABCDA
R EGIME NT
ABCDA
THIRT Y
ABCDA
R EGIME NTAL
ABCDA
WI
THOUT
ABCDA
EITHE R
ABCDA
EX
TRACT
ABCDA
FUS ELAGE
ABCDA
TRACT
ABCDA
D ELIVE R '
ABCDA
INS
TRUCT
ABCDA
GR ENADE
ABCDA
DES
TRUCT ION
ABCDA
ERASE
ABCDA r
TWENT Y
ABCDA
OP ERATE
ABCDA '
B
UREAU
. ABCDA
R ESCUE
ABCDA .
WESTW ARD
ABCDA
PR ESIDE NT
ABCDAA
R
EFUGEE
ABCDA
R ESUME
ABCDAA
C
ODEBOO K
ABCDA
D EVICE
ABCDAA
BU
SINESS
ABCDA
D EVISE
ABCDAA
DI
STRESS
ABCDA
GOING
ABCDAA
STRESS
ABCDA
T HOUGH
ABCDAAD
F
ORENOON
ABCDA
C HURCH
ABCDAB
DECIDE
ABCDA
F IGHTI NG
ABCDAB
DECODE
ABCDA
INFLI CT
ABCDAB
SP
EARHEA D
ABCDA
EXT'INGUI SH
ABCDAB
R
EDUCED
ABCDA
INQUI RE
ABCDAB
ENTREN CH
ABCDA
INQUI RY
ABCDAB
ERASER
3-31
nESTRICTE B
REF ID : A56895
MISCELLANEOUS
ABCDAB
GEORGE
ABCDAB
POSTPO NE
ABCDAB
RETIRE
ABCDAB
ES
TIMATI ON
ABCDABA
DECIDED
ABCDABAB
INCLININ G
ABCDABC
M
AINTAIN
ABCDABC
M
AINTAIN ED
ABCDABCEFD
PHOSPHORUS
ABCDABEFA
ENTRENCHE D
ABCDAC
L
ANGUAG E
ABCDAC
ANYWAY
ABCDAC
GOV
ERNMEN T
ABCDAC
I
NSTANT
ABCDAC
I
NSTANT LY
ABCDAC
DI
SPERSE
ABCDAC
RES
TRICTI ON
ABCDAC
PA
TRIOTI C
ABCDACB
CO
NDEMNED
ABCDACDAEFGB
I
NSTANTANEOUS
ABCDACEFDAF
COINCIDENCE
ABCDAD
MOVEME NT
ABCDAD
A
MUSEME NT
ABCDAD
RIGORO US
ABCDADC
S
ANITATI ON
ABCDADEDAFB
INSTITUTION
ABCDADEFEAGC
ANTIAIRCRAFT
ABCDAEA
EXTREME
ABCDAEA
MAXIMUM
ABCDAEAB
SU
ITABILIT Y
ABCDAEABD
UNI
TEDSTATES
ABCDAEAE
PAR
ENTHESES
ABCDAEB
F
IGHTING
ABCDAEB
S
IGHTING
ABCDAEB
RAILROA D
ABCDAEB
REPORTE D
ABCDAEB
RETURNE D
ABCDAEB
TRACTOR ■
ABCDAEB
INS
TRUCTOR
ABCDAEBA
RECORDER
ABCDAEBC
DE
TONATION
ABCDAEBFBDC
U
NIDENTIFIED
ABCDAEBFC
SATISFACT ORY
ABCDAEC
AVERAGE
ABCDAEC
D
ISTRICT
ABCDAEC
OUTPOST
ABCDAECA
TWENTIET H
ABCDAECAB
I
NTERNMENT
ABCDAECB
D
ISTRICTS
PATTERNS— Continued .
ABCDAECD
L
ABORATOR Y
ABCDAECE
OUTPOSTS
ABCDAECFD
EX
AMINATION
ABCDAED
T
RAVERSE
ABCDAEE
ACTUALL Y
ABCDAEE
EXPRESS
ABCDAEE
THIRTEE N
ABCDAEEFAB
THIRTEENTH
ABCDAEFA
OV
ERWHELME D
ABCDAEFAB
INFLICTIN G
ABCDAEFB
P
RESCRIBE D
ABCDAEFBE
0
NEHUNDRED
ABCDAEFC
M
ANUFACTU RE
ABCDAEFC
PR
ESIDSNTI AL
ABCDAEFC
D
ISTRIBUT E
ABCDAEFCA
D
ISTRIBUTI NG
ABCDAEFCA
D
ISTRIBUTI ON
ABCDAEFD
F
LASHLIGH T
ABCDAEFD
C
ONTROVER SY
ABCDAEFD
A
SCENSION
ABCDAEFD
WINDWARD
ABCDAEFDB
RESTRICTE D
ABCDAEFDE
RESTRICTI ON
ABCDAEFE
PAR
ENTHESIS
ABCDAEFE
RETURNIN G
ABCDAEFEGE
RE
SPONSIBILI TY
ABCDAEFF
REDCROSS ■
ABCDAEFGAHB
INSPIRATION
ABCDAEFGC
REGARDING
ABCDAEFGD
RESTRAINT
ABCDAEFGFE
TR
ANSPACIFIC
ABCDAEFGHC
TWENTYFIVE
ABCDAEFGHFBC
.
CONSCRIPTION
ABCDBA
PR
ACTICA L
ABCDBA
W
ATERTA NK
ABCDBA
DIV
EBOMBE R
ABCDBA
ENGINE
ABCDBA
S
ENTINE L
ABCDBA
R
EVOLVE
ABCDBA
S
ITUATI ON
ABCDBAA
ENGINEE R
ABCDBAAEDBC
ENGINEERING
ABCDBAB
LIABILI TY
ABCDBAD
RE
TALIATI ON
ABCDBAEAD
D
ISPOSITIO N .
ABCDBAEBE
U
NEXPENDED
ABCDBBA
ANTENNA
ABCDBBA
D
ISCUSSI ON
ABCDBBDEA
TRA
NSMISSION
REGTRICTEB - 3.32
REF ID: A5 68 95
HEOTRICTED
MISCELLANEOUS PATTERNS— Continued
ABCDBCAEB
INTENTION
ABCDCEBA
ELIGIBLE
ABCDBCEA
A ERODROME
ABCDCECA
D ESTITUTE
ABCDBEA
INCENDI ARY
ABCDCECDA
CO NSTITUTIN G
ABCDBEA
PR OTECTIO N
ABCDCEFGAB
PHOTOGRAPH Y
ABCDBEA
IN TERCEPT
ABCDCEFGCA
DEM OBILIZATIO N •
ABCDBEAB
IN TERCEPTE D
ABCDCEFGCA
M OBILIZATIO N
ABCDBEAE
C ONTINUOU S
ABCDDA
R ECOMME ND
ABCDBEAFB
INVENTION
ABCDDA
T 3 OBACCO
ABCDBEAFCDB
QU ARTERMASTER
ABCDDA
SHELLS
ABCDBEAFD
INCENTIVE
ABCDDAB
B EACHHEA D
ABCDBEAFD
INTENSIVE
ABCDDAEACBE
INEFFICIENC Y
ABCDBECA
E NCIRCLIN G
ABCDDAEFAF
R ECOMMENDED
ABCDBEFAGABC
ENTANGLEMENT
ABCDDAEFGHICE
R ECOMMENDATION
ABCDBEFAGEB
TEMPERATURE
ABCDDEA
DROPPED
ABCDBEFBA
DECREASED
ABCDDEA
AI RSUPPOR T
ABCDBEFCDAB
C ONTINUATION
ABCDDEA
A RTILLER Y
ABCDBEFGA
YESTERDAY
ABCDDEAEC
COEFFICIE NT
ABCDBEFGAB
ARMOREDCAR
ABCDDECDFA
SCHOOLHOUS E
ABCDBEFGBCHIA
DISTINGUISHED
ABCDDEFCGHA
MI SCELLANEOUS
ABCDBEFGHA
P ERFORMANCE
ABCDDEFEACGE
CLASS I FI C ATI ON
ABCDCA
AIRCRA FT
ABCDDEFGGEDBA
R ECONNAISSANCE
ABCDCA
CRITIC'
ABCDEA
AERONA UTICS
ABCDCA
CRITIC AL
ABODE A
R AILHEA D
ABCDCA
D EFICIE NT
ABCDEA
AIRPLA NE
ABCDCA
ENGAGE
ABCDEA
AMBULA NCE
ABCDCA
P OSITIO N
ABCDEA
CO ASTGUA RD
ABCDCA
PR OVISIO N
ABCDEA
M ATERIA L
ABCDCA
FI REALAR M
ABCDEA
S ATURDA Y
ABCDCAAC
PHILIPPI NES
ABCDEA
C AUSEWA Y
ABCDCAB
ANTITAN K
ABCDEA
N AUTICA L
ABCDCABCA
I NDEPENDEN T
ABCDEA
BLOCKB US TER
ABCDCAC
CRITICI SE
ABCDEA
ME CHANIC
ABCDCAC
CRITICI SM
ABCDEA
CHEMIC AL
ABCDCAD
OPINION
ABCDEA
CONDUC T
ABCDCAEAB
ENGAGEMEN T
ABCDEA
DISLOD GE
ABCDCAEB
P OSITIONS
ABCDEA
DOWNED
ABCDCAED
D EFICIENC Y
ABCDEA
B ECAUSE
ABCDCAED
PR OVISIONS
ABCDEA
D ECIPHE R
ABCDCAEFD
CHARACTER
ABCDEA
D ECLARE
ABCDCAEFDGHEGA
CHARACTERISTIC
ABCDEA
OBJ ECTIVE
ABCDCBABC
IN TERPRETER
ABCDEA
L ECTURE
ABCDCBCEA
HO STILITIES
ABCDEA '
V EHICLE S
ABCDCEA
BRI DGEHEAD
ABCDEA
ENCODE
ABCDCEA
M EDICINE
ABCDEA
COMP ENSATE
ABCDCEA
D EFINITE
ABCDEA
ENTIRE
ABCDCEA
S EPARATE
ABCDEA
R EPLACE
ABCDCEA
SURPRIS E
ABCDEA
R EPULSE D
ABCDCEAFC
QU ALIFICATI ON
ABCDEA
CONSID ERABLE
ABCDCEAFE
P ERSISTENT
ABCDEA
INT ERPOSE
REOTRICTED
3-33
REF ID: A5 68 95
MISCELLANEOUS PATTERNS— Continued
ABCDEA
S ERVICE
ABCDEABFD
NATIONALI SM
ABCDEA
EUROPE
ABCDEABFDC
NATIONALIT Y
ABCDEA
EUROPE AN
ABCDEAB FE
MARKSMANS HIP
ABCDEA
EXCITE
ABCDEABFFGHD
SHARPSHOOTER
ABCDEA
T HROUGH
ABCDEABFGDHF
W ARDEPARTMENT
ABCDEA
IDENTI CAL
ABCDEAC
AUTOMAT IC
ABCDEA
IDENTI FY
ABCDEAC
AI RCONTRO L
ABCDEA
INHABI TED
ABCDEACFB
ANTEDATIN G
ABCDEA
D IRECTI ON
ABCDEAD
CONTACT
ABCDEA
MEDIUM
ABCDEAD
V ICTORIO US
ABCDEA
SY NCHRON IZE
ABCDEAD
C RUISERS
ABCDEA
JU NOTION
ABCDEADFD
THREATENE D
ABCDEA ' '
CO NFIDEN T
ABCDEAE
ENCODED
ABCDEA
NOTHIN G
ABCDEAE
P ERMANEN T
ABCDEA
E NTRAIN
ABCDEAE
FORTIFI ED
ABCDEA
L OCATIO N
ABCDEAE
REQUIRI NG
ABCDEA
REV OLUTIO N
ABCDEAEFGC
TRADITIONA L
ABCDEA
DEC ORATIO N
ABCDEAFA
R EPLACEME NT
ABCDEA
T ORPEDO
ABCDEAFAGE
EXCITEMENT
ABCDEA
OVERCO MING
ABCDEAFAGHEAID
IDENTIFICATION
ABCDEA .
T RAILER S
ABCDEAFB
CLERICAL
ABCDEA
T RAWLER
ABCDEAFB
INVASION
ABCDEA
DI RECTOR
ABCDEAFBC
RESOURCES
ABCDEA
REPAIR
ABCDEAFC
DES IGNATION
ABCDEA
NO RTHWAR D
ABCDEAFC
RES IGNATION
ABCDEA
C RUISER
ABCDEAFC
CO NFIDENTI AL
ABCDEA
I SLANDS
ABCDEAFD
D IMENSION
ABCDEA
STRIPS
ABCDEAFE
ADJUTANT
ABCDEA
SUNRIS E
ABCDEAFE
INTERIOR
ABCDEA
TARGET
ABCDEAFE
I NFLUENCE
ABCDEA
NOR THEAST
ABCDEAFF
R EADINESS
ABCDEA
THREAT
ABCDEAFGA
.D ECIPHERME NT
ABCDEA
NOR THWEST
ABCDEAFGAFB
MEDIUMBOMBE R
ABCDEA
TWELFT H
ABCDEAFGD
LEGISLATI ON
ABCDEA
L UMINOU S
ABCDEAFGE
CO MPARTMENT
ABCDEAA
EIGHTEE N
ABCDEAFGEE
SMOKESCREE N
ABCDEAAE
SUBMISSI ON
ABCDEBA
DELAYED
ABCDEAAFED
EIGHTEENTH
ABCDEBA
D ETONATE
ABCDEAB
INVADIN G
ABCDEBA
INDEMNI TY
ABCDEAB
F LEXIBLE
ABCDEBA
D ISPERSI ON
ABCDEAB
NATIONA L
ABCDEBA
RECOVER
ABCDEAB
REQUIRE
ABCDEBA
SURPLUS
ABCDEAB
RESTORE D
ABCDEBAB
ARBITRAR Y
ABCDEAB
OU TSKIRTS
ABCDEBAED
ARBITRATI ON
ABCDEABA
DEMANDED
ABCDEBFA'
B RIGADIER
ABCDEABD
IMPEDIME NTA
ABCDEBFAGA
ENCOUNTERE D
ABCDEABE
AT OMICBOMB
ABCDEBFCAGBF
INTERNATIONA L
ABCDEABF
REPAIRED
ABCDEBFDGA
NAVIGATION
ABCDEABFB
REQUIREME NT
ABCDEBFGAF
H EADQUARTER S
3-34
REF ID: A5 68 95
liEfiTDICTEfr
M 1SCEU, A.NEOUS PATTERNS— Continued
ABCDEBFGHA
R ESPONSIBLE
ABCDEEA
ENROLLE D
ABCDEBFGHBCGIA
NATURALIZATION
ABCDEEA
P ERSONNE L
ABCDECA
E NLISTIN G
ABCDEEA
IMPASSI BLE
ABCDECA
PRINCIP AL
ABCDEEA
IMPOSSI BLE
AB.CDECA
PRINCIP LE
ABCDEEACB ,
S IGNALLING
ABCDECA
SKIRMIS H
ABCDEEAFDBC
INTELLIGENT
ABCDECAB
I NTERMENT
ABCDEEAFDBGD
INTELLIGENCE
ABCDECAC
I NTERVENE
ABCDEEDFGBA
RECONNOITER
ABCDECACFE
M AINTENANCE
ABCDEEDFGBAFE
RECONNOITERIN G
ABCDECAFCDA
TRANSATLANT IC
ABCDEEFAB 1
ENROLLMEN T
ABCDECBA
NEGLIGEN T
ABCDEEFAB
C ONFESSION
ABCDECBA
REVOLVER
ABCDEEFAE
EMBASSIES
ABCDECBA
P ROTECTOR
abcdeefdgfa'
DISAPPEARED
ABCDECBAFB
NEGLIGENCE
ABCDEEFGCAHB
INTERRUPTION
ABCDECCFA
DISCUSSED
ABCDEFA
C ABLEGRA M
ABCDECDCAFC
I NTERFERENCE
ABCDEFA
AMERICA N
ABCDECFA
ENCIRCLE
ABCDEFA
C AMOUFLA GE
ABCDECFA
EVACUATE
ABCDEFA
CHRONIC AL
ABCDECFBA
SEAPLANES
ABCDEFA
CONFLIC T
ABCDECFEA
STANDARDS
ABCDEFA
DIS CREPANC Y
ABCDEDA
N EWSPAPE R
ABCDEFA
S EABORNE
ABCDEDA
MARITIM E
ABCDEFA
EMPLOYE R
ABCDEDA
CO NTRABAN D
ABCDEFA
ENCIPHE R
ABCDEDA
C OALITIO N
ABCDEFA
ENFORCE
ABCDEDA.
BA ROMETER
ABCDEFA
ENLISTE D
ABCDEDA
GY ROMETER
■ ABCDEFA
D EPLOYME NT
ABCDEDA
HYD ROMETER
ABCDEFA
EQUIPME NT
ABCDEDA
HYG ROMETER
ABCDEFA
FIGHT ERPLANE
ABCDEDA
PSYCH ROMETER
ABCDEFA
ESCORTE D
ABCDEDAB
C ONDITION
ABCDEFA
D ESCRIBE
ABCDEDAC
REC OGNITION
ABCDEFA
J ETPLANE
ABCDEDAFC
N EWS PAPERS
ABCDEFA
EXCLUDE
ABCDEDFA
DICTATED
ABCDEFA
INCLUSI VE
ABCDEDFA
EXCAVATE
ABCDEFA''
LOGICAL
ABCDEDFA
EXHIBITE D
ABCDEFA
F ORMATIO N
ABCDEDFAC
ANTICIPAT E
ABCDECA
T RANSFER
ABCDEDFAC
CLEARANCE
ABCDEFA
REGULAR
ABCDEDFACDGB
ANTICIPATION
ABCDEFA
P RISONER
ABCDEDFCAB
INTERESTIN G
ABCDEFA
SAILORS
ABCDEDFCGAHB
INAUGURATION
ABCDEFA
SECTORS
ABCDEDFDA
ARTIFICIA L
ABCDEF^
SERIOUS LY
ABCDEDFDEAB
. C ONSTITUTION
ABCDECA
E STABLIS H
ABCDEDFDGHAIF
CHRONOLOGICAL
ABCDgFA
TONIGHT
ABCDEDFGA
PR OCLAMATIO N
ABF0EFAA
EMPLOYEE
ABCDEDFGA
P RELIMINAR Y
A2CDEFAAF
T RANSFERRE D
ABCDEDFGABHED
INDETERMINATE
ABCDEFAAGC
T RANSFERRIN G
ABCDEDFGADB
P RELIMINARIE S
ABCDEFAB
INCLUDIN G
ABCDEDFGHAGD
ADMINISTRATI VE
ABCDEFAB
RADIOGRA M
ABCDEDFGHAGDIE
ADMINISTRATION
ABCDEFAB
P REMATURE
r.nitmntnmWTL
3-35
REF ID: A5 68 95
M ISCELLANEOUS PATTERNS— Continued
ABCDEFABA
EMPLACEME NT
ABCDEFBABGHD
MEASUREMENTS
ABCDEFAC *
INTEGRIT Y
ABCDEFBGA
ENDURANCE
ABCDEFAC
P RISONERS
ABCDEFBGBA
DECIPHERED
ABCDEFACB
IN TRODUCTOR Y
ABCDEFCA
ESTIMATE
ABCDEFACD ,
ALTERNATE
ABCDEFCA
NORTHERN
ABCDEFACGF
ALTERNATIN G
ABCDEFCAB
ESTIMATES
ABCDEFAD
CONTRACT
ABCDEFCAD
D OMINATION
ABCDEFAD
D ESTROYER '
ABCDEFCAGFC
ESTIMATEDAT
ABCDEFAD
INTERVIE W
ABCDEFCBA
DETONATED
ABCDEFAD
OPERATOR
ABCDEFCCFA
DISTRESSED
ABCDEFAD
FI RECONTRO L
ABCDEFCEA
DISPERSED
ABCDEFAD
P ROCEDURE
ABCDEFCGA
. ELABORATE
ABCDEFADB
D ESTROYERS’
ABCDEFDA
D EPARTURE
ABCDEFADF
T RANSVERSE
ABCDEFDAB
C USTOMHOUS E
abcdefae
D ISCONTIN UE
ABCDEFDBAB
INTEKVENIN G
ABCDEFAEGHEC
D ISCONTINUANC E
ABCDEFDBCAGB
INTERVENTION'
ABCDEFAF
EXPANDED
ABCDEFDEAB
INTERFERIN G
ABCDEFAF
I MPROVEME NT
ABCDEFDGAB
DEM ONSTRATION .
ABCDEFAFCD
R ADIOSTATIO N
ABCDEFDGAHCD
INTERMEDIATE
ABCDEFAGA
ENCIPHERE D
ABCDEFDGHA
HYDROGRAPH IC
ABCDEFAGAB '
ENFORCEMEN T
ABCDEFEA
R EINSTATE
ABCDEFAGB
AEROPLANE
ABCDEFEAB
F INGERPRIN T
ABCDEFAGB
D ETACHMENT
ABCDEFEAGACE
R EINSTATEMENT
ABCDEFAGB
INFLATION
ABCDEFEAGDB
CERTIFICATE
ABCDEFAGB .
REINFORCE
ABCDEFECACD
THERMOMETER
ABCDEFAGB
TRAJECTOR Y
ABCDEFECAE
CONFERENCE
ABCDEFAGBDB
REIMBURSEME NT
ABCDEFEDCGCAHB
‘ INTERPRETATIOl
ABCDEFAGBHBD
REINFORCEMEN T
ABCDEFEFA
C OMPETITIO N
ABCDEFAGC
INTERDICT
ABCDEFEGA
D EMOBILIZE
ABCDEFAGCAHB
INTERDICTION
ABCDEFEGA
C OMPUTATIO N
ABCDEFAGE
D EPARTMENT
ABCDEFFA
UN DERSTOOD
ABCDEFAGEC
D EPARTMENTA L
ABCDEFFA
IMPRESSI ON
ABCDEFAGFD
REGISTRATI ON
ABCDEFFAGE
IMPRESSIVE
ABCDEFAGHAB
ENCIPHERMEN T
ABCDEFFEDAGBC
INSTALLATIONS
ABCDEFAGHEBC
CONFISCATION
ABCDEFFGAB
C ONGRESSION AL
ABCDEFAGHFD
INVESTIGATE
ABCDEFGA
DISARMED
ABCDEFAGHFAIB
INVESTIGATION
ABCDEFGA
M ECHANIZE D
ABCDEFAGHFAIBE
INVESTIGATIONS
ABCDEFGA
T ECHNIQUE
ABCDEFAGHIF
B REAKTHROUGH
ABCDEFGA
R ECOGNIZE
ABCDEFBA
DECLARED
ABCDEFGA
ENFILADE
ABCDEFBA
- DEPARTED
ABCDEFGA
EQUALIZE
ABCDEFBA
DEPLOYED
ABCDEFGA
EQUIPAGE
ABCDEFBA
DEPORTED
ABCDEFGA
EQUIVALE NT
ABCDEFBA
DETACHED
ABCDEFGA
D ESIGNATE
ABCDEFBA
EMPLOYME NT
ABCDEFGA
EXCHANGE
ABCDEFBA
ENTRAINE D
ABCDEFGA
GROUPING
ABCDEFBA
REGISTER
ABCDEFGA
GUARDING
ABCDEFBA
P ROJECTOR
ABCDEFGA 1
INSECURI TY
ABCDEFBAB
MEASUREME NT
ABCDEFGA*
D IPLOMATI C
RESTRICTED
REF ID: A5 68 95
ABCDEFGA
ABCDEFGA
ABCDEFGA
ABCDEFGA
ABCDEFGA
ABCDEFGA
ABCDEFGA
ABCDEFGA
ABCDEFGAB
ABCDEFGAB
ABCDEFGAB
ABCDEFGABF
ABCDEFGAC
ABCDEFGAC
ABCDEFGACB
ABCDEFGAD
ABCDEFGAD
ABCDEFGADG
ABCDEFGAEHBC
ABCDEFGAFE
ABCDEFGAG
ABCDEFGAHB
ABCDEFGAHCGIDE
ABCDEFGBA
ABCDEFGBA
ABCDEFGBA
ABCDEFGBA
ABCDEFGBA
ABCDEFGBACAHGD
ABCDEFGBAE
ABCDEFGBHA
ABCDEFGBHIAKC
ABCDEFGCAG
ABCDEFGCHEA
ABCDEFGDAHB
ABCDEFGDAHBC
ABCDEFGDBFHA
ABCDEFGDHAIC
MISCELLANEOUS
E NTRUCKIN G j
NUMBERIN G‘ /
OBJECTIO N /
- OPERATIO N ,
SOLDIERS
DI SPATCHES /
WITHDRAW /
WITHDREW
D ESPATCHES
U NDERSTAND
WITHDRAWI NG
ENLISTMENT
I NSTRUMENT
F OUNDATION
I NSTRUMENTS
SOUTHEAST
SOUTHWEST
SOUTHWESTE RN
CONSTRUCTION
IMPRACTICA BLE
WITHDRAWA L
'INSPECTION
RECONSTRUCTION
DESCRIBED
DESTROYED
DETRAINED
REMAINDER
TRANSPORT
TRANSPORTATION
TRANSPORTS
ESTABLISHE D
ESTABLISHMENT
CONFIDENCE
RANGEFINDER
INSTRUCTION
INSTRUCTIONS
CE NTRALIZATION
OBSTRUCTIONS
PATTERNS— Continued
ABCDEFGDHFAE
ABCDEFGEA
ABCDEFGEHA
ABCDEFGFABF
ABCDEFGFAG
ABCDEFGGAG
ABCDEFGHA
ABCDEFGHA
ABCDEFGHA
ABCDEFGHA
ABCDEFGHA''
ABCDEFGHA
ABCDEFGHA
ABCDEFGHAB
ABCDEFGHADB
ABCDEFGHAGC
ABCDEFGHBA
ABCDEFGHBA
ABCDEFGHBIKA
ABCDEFGHCAEB
ABCDEFGHCAEB
ABCDEFGHDAB
ABCDEFGHDGCA
ABCDEFGHDIKA
ABCDEFGHEEHA
ABCDEFGHFA
ABCDEFGHFCAG
ABCDEFGHIA
ABCDEFGHIA
ABCDEFGHIA
ABCDEFGHIA B
ABCDEFGHIAE
ABCDEFGHIAF
ABCDEFGHIDAB
ABCDEFGHIFKA
ABCDEFGHIGBA
ABCDEFGHIJDA
ORGANIZATION
H EAVYBOMBE R
D ESCRIPTIVE
I NCOMPETENCE
I NCOMPETENT
H EAVYLOSSES
CONSPIRAC Y
DOMINATED
C ENTRALIZE
EXCLUSIVE
EXPANSIVE
EXPLOSIVE
MECHANISM
C ONSUMPTION
INFORMATION
CONVALESCEN T
DESIGNATED
DESPATCHED
DISORGANIZED
INTRODUCTION
D ISCREPANCIES
C ONFIRMATION
NORTHWESTERN
REVOLUTIONAR Y
COUNTERATTAC K
D EMONSTRATE
AGRICULTURAL
DISPATCHED
OBSERVATIO N
SUBMARINES
C ONVERSATION
C OMPENSATION
R 0 ADJUNCTION
C ONSIDERATION
SEARCHLIGHTS
DEMONSTRATED
' SIMULTANEOUS
' 3-37
- RESTRICTED
RESTRICTED
REF ID : A56895
& DIGRAPHIC IDIOMORPHS : GENERAL
AB AB
-G EN ER
AL AL
AR
NE
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IN IN
G-
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REF ID: A5 68 95
RESTniOTEB -
AB AB
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AN
AM
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AL
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3-39
REF ID : A56895
SC
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AB BA
AB
BA
RD
SH
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LE
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AF
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REF ID: A568 9-5
AB BA
AB — BA
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MI
NE
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PR
AC
TI
CA
BL
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MI
NG
PR
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REF ID : A56895
AB
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BA
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NA
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PL
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MB
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REF ID : A56895
RESTIUCTE &
F. DIGRAPHIC IDIOMORPHS : FOUR-SQUARE 1
( Grouped by number of significant letters in the idiomorphic pattern)
Two letters
A-
A-
A-
A-
A-
—
A-
B
LO
CK
AD
ED
SQ
UA
DR
ON
MO
VE
ME
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NV
AD
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FI
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A-
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10
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NA
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C
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TT
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10
N
CO
NS
TR
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N
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MB
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N
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AB
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NC
E
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N
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MB
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AG
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NS
T
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FT
H
R OA
DJ
UN
CT
10
N
R
AI
LH
EA
D
FI
FT
Y
R
EP
LA
CE
ME
NT
PR
EP
AR
AI
10
N
BR
ID
GE
HE
AD
R
ET
RE
AT
A
SS
AU
LT
V
IC
IN
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Y
S
EV
ER
AL
B
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BA
RD
W
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HD
RA
W
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NC
TI
ON
A
IR
BO
EN
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A
DD
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10
NA
L
CO
NF
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MA
TI
ON
S
EA
BO
RN
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A
MM
UN
IT
10
N
I
NF
OR
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TI
ON
A
DV
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Cl
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CO
ND
IT
10
N
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Cl
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CO
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IT
10
N
PA
TR
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TA
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ME
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MI
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SE
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H
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N
MI
NI
MU
M
AC
TI
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TY
M
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EN
T
NI
HT
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A
TT
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TI
ON
EN
EM
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P
01
HD
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SS
FU
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OR
RO
W
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ET
UR
N
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A-
—
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A-
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QU
ES
T
AR
TI
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AG
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SO
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NF
OR
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N
RE
SI
ST
AN
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R
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NF
OR
CE
ME
HT
A PP
RO
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NO
D
IS
PO
SI
TI
ON
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EN
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FY
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BO
UC
HI
NG
PO
SI
TI
ON
IM
PA
SS
IB
LE
L
AD
NC
HI
NG
SO
UT
H
1
IM
PO
SS
IB
LE
I
MM
ED
IA
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LY
1 See subpar. , Section IX.
nEDTRIGTE D
3-^3
REOTmCTED
REF ID : A56895
Two letters (cont.)
-B
-B
IK
IT
LA.
TE
F
IF
TH
TE
RR
IT
OR
Y
S
IX
TY
M
IS
CE
LL
AN
EO
US
E
LE
VA
TI
ON
E
LE
VE
K
LI
AI
SO
N
DA
MA
GE
MO
RN
IN
G
U
KU
SU
AL
OB
JE
CT
IV
E
C
OL
OK
C
OL
ON
EL
SU
PE
RI
OR
IT
Y
M
or
OR
IZ
ED
OU
TS
KI
RT
S
EQ
UI
PM
EN
T
A
VE
RA
GE
B
AR
RA
GE
AI
RC
RA
FT
AN
TI
AI
RC
RA
FT
RE
MA
IK
R
EQ
UI
RE
ME
NT
M
IS
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KG
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P ER SO m EL
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P LA. TO ON
S UP PL Y
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NA VA LB AS E
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WI ND WA RD
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--
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C
AS
UA
IT
Y
P
AT
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LS
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TL
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HI
PS
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RA
L
W
IL
LA
TT
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RA
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MI
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;io
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NI
TI
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T
RO
OP
SH
IF;
RE
GI
ME
ht
CA
RR
IE
RS'
MI
SS
10
NS
TW
EN
TY
R
EQ
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ST
ED
Three letters
-B
--
—
-B
i
DE
NT
IF
IC
AT
10
N
M
EC
HA
NI
ZE
D
D
EP
LO
YM
EN
T
M
ES
SE
NG
ER
D
ES
TR
OY
ER
A
IR
SU
PP
OR
T
V
IS
IB
IL
IT
Y
ME
SS
EN
GE
R
I
MP
AS
SI
BL
E
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MP
OS
SI
BL
E
A
NT
IA
IR
CR
AF
T
C
0M
MA
ND
IN
G
OP
ER
AT
10
N
PR
IS
ON
ER
PR
OC
ED
UR
E
RE
EN
FO
RC
E
TR
AN
SP
OR
TA
TI
ON
YE
ST
ER
DA
Y
-B
_ —
....
— —
-B
R
EC
OM
ME
ND
ED
HE
AV
YL
OS
SE
S
R
EC
OM
ME
HD
AT
10
N
C
OM
MU
NI
CA
TI
ON
R
EC
ON
NO
IT
ER
IN
G
A- A- A-
A- A A-
-B -B -B
N AV AL BA SE
R EQ UI SI TI ON
RE QU ESTE D
B OM BA RD ME NI'
EL EM EN TS
EN GA GE ME NT
Four letters
AB A- -B
A- AB -B
A- -B A3
H EA DQ UA RT ER S
AD DI TI ON AL
M OR NI NG
EL EV EN
P OS TP OH E
•
A- AB B ,
AB -B A-
SO UT HIT ES T
A- -B -B — A-
CA NC EL
RE CO NN 01 TE R
RE CO NN AI SS AN CE
A- A- -B -B ;
W IT HD RA WA L
A- -B -- AB
AB -B — A-
HI TE RD IC T
AD VA NC ED
A- A A- A-
EN EM YT AIT KS
CO MI AIT DI ITG
A- -B -- A- -B
S AT IS FA CT OR Y
AB — A- -B
A- A B r 3
SI OH TI NC-
RE QU IR EM EN T
A A- C- C-
DI SP AT CK ES
r>
REF ID : A56895
s
HUIUTKIAJ 1 lilD
A- C- A- C-
Four letters (cont.)
-B A- — AB
-B -D -D -B
RO AD JU NC TI ON
-B AB A-
U NS UC CE SS" FU L
-B A A- -B
AI RS UP PO RT
-B -D D -B
DI SP OS IT 10 N
P OS IE 10 N
PR ES EN T
RE PR ES EN %
-B A- AB
UE DI ,UM BO MB ER
-BA-'f-BA-
VI SI BI LI TY
-B A AB
IN ST RU C T 10 N
C ON ST RU CT 10 N
-B — A- AB
F IG HE ER PL AN ES
-B — A AB
E ST AB LI SH ME NE
-B B A- A-
EN CO UN TE RE D
-B B -D -D
RE IN FO RC EM EN T
RE PE AT ED
-B A- A- -B
IN FO m AT 10 N
~B A- A- -B
DE ST RO YE R
-B A- -B — A-
IN' ST AL IA TI ON
-B -D -B D
UN ID EN TI FI ED
CR OS SR OA DS
/
Five letters
A- -B AB B
-B A- A AB
-B -D D -B -D
NA VA LA TT AC K
DI ST RI BU TI OH
IN ST RU CT 10 NS
A- -B B AB
-B A- -B AB
R EC ON NA IS SA NC E
RE PL AC EM EN T
i
Six letters
AB CB C- A- | A- A- -B AB A- | A CB A CB
RE QU IS IT 10 N " '
A- CB — A- CB
C ON DI TI ON Q UA RT ER MA ST ER A DM Hi IS TR AT IV E
RA DI OG RA M
A- CB — CB A-
SC HO OL HO US E
ID EN TI FI CA TI ON
-B AE AD -D
P OS IT 10 NS
AB -D -D AB
3-45
CONFIDENTIAL
REF ID : A56895
APPERDIX 10
COJTOfllCATIOB IffriCLLIGEtlCE 0EEHATI01TS
I
Paragraph
Communication intelligence pi'ocessea
Intox*cej)tio», radio direction finding, and radio position finding.*.
Radio fingerprinting and Morse operator analysis
Traffic analysis
Cx'yptanalysis
Other intelligence sources
Time needed for cryptanalysis and its dependent factors.
Ciryptanalytlc records and reports
Illustrative example of a technical report
1 . Communication intelligence processes . The principal processes
of communication intelligence operations are as follows:
a. Interception of communication signals or messages and forward-
ing raw traffic^ to communication intelligence centers for study*
h. Radio direction finding and radio position finding operations;
Identification of transmitters and radio operators by means of radio
fingerprinting and Morse operatox' analysis, respectively.
c. Traffic analysis, or the study of the external characteristics
of communications , without recourse to cryptanalysis of the message
texts .
d. Cryptanalysis or solution of the texts of messages.
e. Translation and emendation of the message texts.
f . large-scale production or exploitation of communication intel-
ligence, after the Initial break-in.
g. Evaluation of information, yielding military intelligence.
, h. Collation, correlation and comparison of communication intel-
ligence with other intelligence sources.
i . Distribution of communication. intelligence to consumers .
2. Interception, radio direction finding, and radio position find -
ing . --a . Messages transmitted by radio can be manually copied or auto-
matically recorded by suitably adjusted radio apparatus located within
range of the transmitter. Some messages transmitted over wire lines
can likewise be manually copied or automatically recorded by special
apparatus suited for the purpose. Correspondents have no way of know-
ing whether or not radio transmissions are being copied by the enemy,
since the interception does not interfere in the slightest degree j with
4
1 haw traffic is unprocessed intercepted traffic .
CONFIDENTIAL
10-1
(Appendix to NS A text, "Military
Crypt analytics, Parti", Dec 1952)
vo CO-<3 cvvn 4=-W ro H
CONFIDENTIAL REF ID : A56895
signals being transmitted. Interception of wire traffic is much more
difficult than of radio, mainly because the equipment either must be
located very near the wire line, or connected directly to it.
b. It is possible to determine, with a fair degree of accuracy,
the direction of a radio transmitter from a given location and, by estab-
lishing the direction from two or more locations, it is possible to deter-
mine the geographical location of the transmitter. The science which
deals with the means and methods of determining the direction in which a
radio transmitter lies is called radio direction finding ; the method of
determining the geographical location of a radio trar emitter, by the use
of two or more direction-finding installations , is called radio position
finding.
3 . Radio fingerprinting and Morse operator analysis . — a . Radio
fingerprinting is one of the valuable adjuncts of signal analysis, a
communications -engineering sister of traffic analysis. Radio finger-
printing consists of the analysis of the characteristics of the emissions
of an individual radio transmitter by means of oscillograms of the emit-
ted radio waves . The oscillograms of the emissions of unidentified radio
stations are compared with those of known transmitters or radio stations,
and thus it is possible to equate different call signs or different fre-
quencies which have been used by the same transmitting station. Radio
fingerprinting is normally not considered conclusive in itself, but is
correlated with other analyses or confirmations .
b. Another valuable adjunct of communication intelligence operations
is Morse operator analysis . This analysis deals with the radio operators'
characteristics when hand-sending is used; the analysis is based on the
relative lengths and spacing of the dots and dashes composing the various
Morse characters . It is a rarity when a radio operator will transmit
a Morse character perfectly, i.e., moke the dashes the correct length
in respect to the dots, without any individuality (known as the "fist"
or "swing") in the sending. Most operators do have certain individual
characteristics or tendencies in the sending of certain Morse characters.
In past decades, radio operators have identified characteristic "fists"
of other operators based on the aural recognition of the rhythm of cer-
tain Morse characters . This art has been made more scientific through
the use of actual physical measurement and through the assignment of a
classificatory coding to the individualities present in the undulator-
tape recording^ of a Morse transmission. By matching measurements, indi-
vidual radio operators may be identified, in spite of changes of call
signs and other elements of the transmission.
U ♦ Traffic Analys is . — a . A great deal of information of military
value can be obtained by studying signal communications without solving
encrypted messages constituting the traffic . The procedure and the meth-
ods used have yielded results of sufficient importance to warrant the
^ Such recordings take the form of a wavy inked line on a paper tape,
being a visual representation of the dots and dashes as transmitted.
CONFIDENTIAL
10-2
CONFIDENTIAL
REF ID: A5 68 95
application of a special tem to this field of study; namely', traffic
analysis , which is the study of signal coxmnunications and intercepted or
monitored traffic for the purpose of gathering military information with
out recourse to cryptanalysis .
I
b. In general terms, traffic analysis is the careful inspection
and study of signal communications for the purpose of penetrating cam-
ouflage superimposed upon the communication network for purposes of
security . Specifically, traffic analysis reconstructs radio communica-
tion networks by: (l) noting volume, direction, and routing of messages
(2) correlating transmission frequencies and schedules used among and
within the various networks; (3) determining directions in which trans-
mitters lie, by means of radio direction finding; (h) locating trans-
mitters geographically, by radio position finding; (5) developing the
system of assigning and changing radio call signs; and (6) studying all
items that constitute messages originated by operators and exchanged
among themselves on a radio net.
/
< 2 . From a correlation of general and specific information derived
by means of the foregoing procedures, traffic analysis is able not only
to ascertain the geographic location and disposition of troop3 and mili-
tary units (technically called "Order of Battle") and important troop
movements, but also to predict with a fair degree of reliability the
areas and extent of Inuaedintely pending or future activities . Traffic
analysis procedures are followed to obtain information of value con-’
cerning the enemy, and to determine what information concerning our
own forces is made available to the enemy through our own signal com-
munications . Specifically, enemy military plans and operations may be
revealed as follows:
(1) Unit movements and preparations for military activity my be
indicated by rising and falling traffic volumes and changes in the
structure of the network.
(2) The military function of a network may be revealed by the
characteristic traffic pattern which results from transmissions inci-
dental to planning, supply, or transportation.
(3) Change of grouping, disposition of forces and fleets, and
probable tactical developments may be manifested in the redeployment
of the radio stations which serve military elements.
d. These very important results are obtained without actually
reading the texts of the intercepted messages; the solution and trans-
lation of messages are the functions of cryptanalysis and not traffic
analysis. However, the cryptanalyst is frequently able to make good
use of bits of information disclosed by traffic analysis such as faults
noted in message routing and errors in cryptography causing messages
to be duplicated or canceled. Cryptanalysis can provide important
J Such operators ' communications are termed "chatter" or simply
h chat ."
CONFIDENTIAL
10-3
CONFIDENTIAL
REF ID: A5 68 95
information for traffic analysis, since the solution of messages often
yields data on impending changes in signal communication plans, opera-
ting frequencies and schedules, etc. Cryptanalysis also yields data
on specific channels, networks, or circuits which are most productive
of intelligence, so that effective control and direction of intercept
agencies for maximum results can be achieved.
2 . Cryptanalysis ♦ The most important steps of practical, opera-
tional cryptanalysis are listed below. These steps are more or less in
the order in which they are followed, but in particular cases some of
these steps may be interchanged, or omitted entirely.
a. The study of patent characteristics of message texts.
b . The study of any available collateral information, including
that obtained from previous solutions .
c . The search for and study of indicators .
d. The determination of the type of cryptosystem used.
e. The separation of the traffic into groups of messages in the
same or related keys .
f . The search for repetitions within and between messages.
g. The study of the beginnings and endings of messages.
h . The preparation of statistical counts of letters , groups , etc .
i . The reduction of the encrypted texts to simplest terms .
. The test for probable words , stereotypes , isologs , etc .
k . The recovery of the plain texts .
6 . Other Intelligence Sources . In addition to (l) traffic analysis
and (2) cryptanalysis as means of obtaining information relating to com-
munications, further data my be obtained (3) by the use of secret agents
for espionage, (4) by the capture and interrogation of prisoners, (5) by
the capture of headquarters or command posts with records more or less
intact, and (6) by defection or carelessness on the part of personnel who
handle communications. Of these six main sources, traffic analysis and
cryptanalysis are the most valuable, due in great part to their reliabil-
ity; they may be likened to "reading the innermost thoughts of the enemy' 1
The amount of vital information they furnish cannot be accurately esti-
mated as it fluctuates with time, place, circumstances, equipment, and
personnel. For most effective operation, the results of both cryptanal-
ysis and traffic analysis can be fitted together to yield a unified
picture of the communications scheme. Therefore, if all transmitting
■ CONFIDENTIAL
10-U
CONFIDENTIAL
REF ID : A56895
stations can "be located quickly and If all communications can "be inter-
cepted and solved, extremely valuable information concerning strength,
disposition of forces , and proposed moves will be continually available.
7 . Time needed for cryptanalysis and Its dependent factors .--
a. In military operations time is a vital element. The influence
or effect that analysis of military cryptograms may have on the tactical
situation depends on various time factors.
b. Of these factors, the following are the most important:
(1) The length of time necessary to transmit intercepted enemy
cryptograms to solving headquarters . This factor is negligible only
when signal communication agencies are properly and specifically
organized to perform this function.
(2) The 3.ength of time required to organize raw materials, to make
traffic analysis studies and to solve the cryptograms , and the time re-
quired to make copies, tabulate, and record data.
(3) The nature of Information disclosed by traffic analysis studies
and solved cryptograms; whether it is of immediate or operational impor-
tance in impending action, or whether it is of historical Interest only
in connection with past action.
(k) The length of time necessary to transmit information to the
organization or bureau responsible for evaluating the information.
Only after information has been evaluated and correlated with informa-
tion from other sources does it become Intelligence .
(5) The length of time necessary to transmit the resulting intelli-
gence (military, naval, air, etc.) to the agency or agencies responsible
for tactical operations, and the length of time necessary for the agency
to prepare orders for the action determined by the intelligence and to
transmit such orders to the combat units concerned. The last sentence
under (l) above applies here also.
£. Of the factors mentioned in b above, the only one of direct
interest in this text is the length of time required to solve the crypto
grams . This is subject to great variation, dependent upon other factors
of which the following are the most important:
(l) The degree of resistance of the system to cryptanalytie attack.
This is dependent upon the technical soundness of the system itself, the
technical soundness of the regulations and procedures governing the use
of the system, and the extent to which cipher clerks follow these regu-
lations and procedures .
k
Often referred to as f inished intelligence .
CONFIDENTIAL
10-5
CONFIDENTIAL
REF ID : A56895
(2) The volume of cryptographic text available for study. As a
rule, the greater the volume of text, the more easily and speedily it
can be solved. A single cryptogram in a given system may present an
almost hopeless task for the cryptanalyst, but if many cryptograms of
the same system or in the same or closely related specific keys are
available for study, the solution may be reached in a very short time .
(3) The number, skill, and efficiency of organization and coopera-
tion of communication intelligence unit3 assigned to the -work. Crypt-
analytic units range in size from a comparatively few persons in the
forward echelons to many persons In the rear echelons . Such organization
avoids duplication of effort and, especially in forward areas where spot
intelligence is most useful, makes possible the quick interpretation of '
cryptograms in already solved systems . In all these units , proper organ-
ization of highly skilled workers is essential for efficient operation.
(4) The amount and character of collateral information and intelli-
gence available to the cryptanalytic organization. Isolated cryptograms,
exchanged between a restricted, small group of correspondents about whom
and whose business no information is available may resist the efforts of
even a highly organized, skilled cryptanalytic organization indefinitely.
If, however, a certain amount of such information is obtained, the situ-
ation aiay be entirely changed. In military operations usually a great
deal of collateral, information is available, from sources indicated in
paragraph 6, above. As a rule, a fair amount of definite information
concerning specific cryptograms is at hand, such as proper names of per-
sons and places, and events in the immediate past or future. ^ Although
the exchange of information between intelligence and cryptauzly s.V* staffs
is very important, the collection of information derived from an inten-
sive study of already solved traffic is equally as important because It
yields extremely valuable cryptanalytic intelligence which greatly facil-
itates the solution of new cryptograms from the same sources .
6 . Cryptanalytic records and reports . — a. In practical cryptana-
lytic work the systematization of records and the maintenance of adequate
files are of considerable importance. Likewise, the preparation of clear
and concise reports, both technical and non-technical, is a major facet
of practical cryptanalytic operations .
b . All messages coming into the cryptanalytic section are assigned
a reference number, and a log is kept of these raessages showing pertinent
data such as the call signs, the date and time of interception, the group
count, etc. Duplicate messages (i.e., different intercepts of the same
transmission, or intercepts of retransmissions of the same message) are
stapled together and garbles are corrected. Other records and files are
maintained for special studies; for example, there may be card files on
In this connection, see the remarks on cribs and probable words in
subpars . 2d and 49c .
CONFIDENTIAL
10-6
CONFIDENTIAL
REF ID: A5 68 95
the message indicators^ that have appeared in the traffic, card files of
keys used in past and current systems, etc.
c. Cryptanalytic reports fall into two main categories: (a) tech-
nical reports intended for cryptanalytic personnel designed to give a
summary of the cryptographic features of a system, with the steps that
were taken to diagnose the system and effect a solution} and (h) non-
technical reports destined for intelligence consumers?, which reports
consist for the most part of message decrypts . In the latter category
all decrypts might he furnished verbatim, or complete decrypts of impor-
tant messages only, the rest of the messages being furnished in "gists"
or in condensed form.
O
d. In technical reporting, clarity and detail are paramount. A
complete resume of the diagnostic techniques employed in the identifica-
tion of the system should be included, as well as a comprehensive outline
of the steps taken to arrive at the initial solution. ° it goes without
saying that close attention should be paid to precise cryptologic termi-
nology in all descriptions of methods and techniques, so as to lessen
the chance of ambiguity or possible misunderstanding on the part of the
reader . A cryptologic glossary should he freely consulted in all cases
where there is an element of doubt in the mind of a writer as to the ex-
act meaning of a term he is about to use .
e . In the next paragraph there is found an example of what may be
considered as typical of a cryptanalytic technical report. Of course
there is no fixed standard format for such a report, as the particular
way in which a report is prepared, and the information included therein,
depends upon the circumstances and situation at the time of the report.
However, the hypothetical report in the next paragraph is intended as il-
lustrative of the amount of detail that might be included in a report of
this nature.
, ...
In this connection, the location of groups of a message is desig-
nated by the terms Al, A2, A3 — if reference is made to the first, second
third. . .positions from the beginning of the encrypted text, and by the
terms Uf, Zl, Z2...if reference is made to the last, penultimate, ante-
penultimate . . .positions from the end of the encrypted text .
? These reports are Invariably highly classified, and their dissemina-
tion is strictly controlled on a special distribution list of those who
must have a "need-to-know." This limitation is absolutely essential in
order to protect the information, and prevent drying up the source and •
negating the work of the many weeks, months, or even years that are repre
sented by the fruits of the communication intelligence effort. In this
latter connection, when Information derived through communication Intel-
ligence efforts is included in military intelligence reports, it is dis-
guised in such a way as to protect the source of the information.
o
° For an excellent exposition on the art of technical writing, see
Joseph N. 'Ulman, Jr., Technical Reporting , Eew York, 1952.
9 See also the remarks made in subpar. 47f , on pp. 94-95 •
CONFIDENTIAL
10-7
CONFIDENTIAL
REF ID : A56895
9. Illustrative example of a technical report . The following repre-
sents a hypothetical technical report on the cryptanalysis of a newly-
encountered system:
(CLASSIFICATION)
Special Distribution
REPORT ON THE SOLUTION
OF THE "CALOX " SYSTEM
5 January 19
Copy No.
of copies
I - BACKGROUN D
1. On 12 December 19 , a new discriinmant.CALOX, appeared in the enemy’s
traffic. The discriminant appears in the usual position, the A1 group of the message.
2. Traffic analysis indicates that CALOX traffic is being passed on air defense
nets. From the characteristics of the transmission of this traffic and associated procedures,
it appears that CALOX is an administrative system rather than an operational system. It
also appears that CALOX does not replace an existing system, but rather is a new system
introduced for some special purpose. On the enemy's air defense nets, both cipher and
code systems have been encountered.
3. CALOX traffic was segregated and logged in as received, together with the
worksheet reference numbers assigned to all incoming traffic by the Traffic Handling
Section.
II - PRE L IMINARY A NALYSIS
4. The first step in treating the CALOX system was to complete the plain -component
sequence on one of the messages, on the hypothesis of direct and reversed standard alphabets,
using a strip board for this purpose. (The enemy has used standard alphabets in the past in
one system, changing the juxtaposition of the components after the encryption of every few
letters. ) This disclosed nothing of significance.
5. Uniliteral frequency distributions made for each of the six messages intercepted
on 12 December were flat; the average LC. of 1. 1 indicates that it is most unlikely that
the underlying cryptosystem is a mono alphabetic system involving single -letter cipher units.
However, a rather odd manifestation in the distributions for each message was that C c , Dc,
H c , L c , and Vc were usually consistently predominating, while S c , Yc t and Zc were con-
sistently of very low frequency. No explanation for this phenomenon was forthcoming at
the time.
6. A check was made on previously solved enemy systems used on his air defense
and other nets, to disclose any similarity between the CALOX characteristics and those
of another system; this proved fruitless, as the uniliteral frequency manifestations of CALOX
were unique to that system. A check was also made to find any possible isologs between
CALOX messages and those of another readable system; however, this too proved fruitless,
as did the examination of chatter associated with the CALOX messages in an attempt to
reveal any clues as to the system or to uncover possible cryptographic service messages, etc.
10-8
CONFIDENTIAL
REF ID: A56895
COMFIDEMTlA t r
7. Digraphic distributions were made of the messages of 12 December, but no
unusual phenomena were visible* The approached dial of {$ , and there was no
evidence to suppoit any matching of the rows or columns of the distributions if the
hypothesis of a variant system with a small matrix were assumed.
8. Triliteral frequency distributions were made of each message to disclose
repetitions; these repetitions were undcilined in the messages, and a comparison was
made of those repetitions occurring between messages of the same day. Many short
repetitions of 3, 4 f and 5 letters were disclosed, the number of these repetitions
being considerably above that expected for random; however, no longer repetitions
were uncovered, and the intervals between the repetitions had no common factors.
9. Every day's accumulation of traffic was examined statistically with a view
to revealing possible key changes, and the phenomena in par. 5, above, continued.
When on 19 December the predominant peaks and troughs no longer corresponded to
the norms observed m par. 5, a change of keys was assumed.
10. A typical message in the first key period is given below;
LRZ DE CKS (Intercepted 17 December, on a frequency of 5600 Kcs)
CALOX JOLDJ JLAPP DREEF QXEDZ
OMMYE HQDAH YEMNB VUGHD 3MXOG
FRILM UGBOC DEXJL UBWW TRAFX
DIKQW MCGIW* HRMAF EKGEE FNPOG
TJXAN BLTUR KOTOR CFIH7 QGEKH
LAXVY HEQBX RIKRK YACSV LPOQP
DKIQC MRADN VNUKB TOPBH L±KLH
ODMXT DHONG XHXEL BWXGA LDIGB
in - THE SOLUTION
QIHFN WMGUH DMAYM IMNDY OMZCC
LDHUX MACJV VRNEK LCHEJ DZCDO
LKNPA HSJNE HVCAC OQTHU FJVTH
JEOGM WGUDM XJIJL BWEPK QCUMR
HUJNQ ATBWZ VHERI LHFOQ MLUMX
NOBKU XGLED FHPAG JRRAB JLEBW
EFVTR BGYMA MYQWI FVLEM GLEGH
GCIIM ZQLAC LXODQ
11. The following peculiar sets of similar sequences of cipher letters were
noted during the examination of the 32 messages available in the first key period. The
message reference numbers are given, together with the position in the message of the
first letter of the sequence. (The position given is die text position, excluding the
discriminant. )
Msg No . Pos.
a) 60208 057
61492 216
60317 139
HFIJVTHODK
HFJV OTHDKQ
HUFJVTHDIK
QWMEC GAWHR
AWMEC GWHAR
QWMCGIWHR
C ONFIDENTIAL
10-9
CONFIDENTIAL
REF
ID
*
m *
A56895
b)
60317
123
N
P
A
H
S
J
N
E
H
V
c
A
C
Q T
62350
098
N
P
H
I
S
J
N
0
H
V
c
C
U
Q T
C)
60317
184
J
L
B
W
E
D
K
Q
C
U
M
R
60317
291
J
L
E
B
W
D
K
I
Q
C
M
R
d)
60295
114
T
P
I
Q
K
Z
H
E
H
V
P
U
V
P B
61007
253
T
P
0
Q
K
Z
H
A
H
V
P
E
V
P B
e)
60943
147
H
V
G
G
A
K
W
Q
S
0
V
R
N
62156
064
H
V
U
G
G
K
E
w
Q
s
V
I
R
N
The behavior of the letters comprising these sequences indicates that A c , Ec, Ic, 0 C| and U c ,
most likely are nulls. On this hypothesis, evidence from the lengths of the repetitions now
disclosed, and the intervals between repetitions, indicates a digraphic grouping of the cipher
text. On checking back to the digraphic distributions, it is noted that there are no vowel-
vowel contacts in the cipher text, except for combinations with Y c . Furthermore, in retrospect
it is seen that most of the cipher groups contain l'or 2 vowels, never more; this significance
escaped notice until the near-repetitions above were observed.
12. New digraphic distributions, omitting the 5 vowels, were made for the messages
in the first key period. No matching qualities were manifested in die new distributions; but
this time the (J>2 very closely approximated the ^ ti lus it appeared that, in spite of the limi-
tation of only 21 ciphertext letters remaining after the null vowels were discarded, the system
was basically a digraphic system. (This would not exclude, however, a matrix containing a
few frequent trigraphs or tetragraphs, etc. ) Work sheets were now made for several of the
best messages from the first key period, the messages selected being long ones that existed in
more than one intercept copy so that garbles might be corrected.
13. On 28 December the first message was solved; this was Message #60317 which
was one of the longest, and which was copied by three different intercept operators. One
more cryptographic idiosyncrasy of the CALOX system was now brought to light; that of
the peculiarity of behavior of Y c which had been previously overlooked. This peculiarity
was that Y c was always present in pairs, fairly close together; every Y Q was followed by
another Y , with from 2 to 10 letters intervening. This Y c turned out to be a number
indicator, and the cipher digraphs between the indicators represented single digits.
14. From the original solution, an equivalent digraphic matrix was reconstructed
with the consonant coordinates in normal alphabetical order, as shown below;
10-10
CONFIDEN Tt A fc
REF ID: A5 68 95
C ONFIDENTIAL
2d Letter
Noting evidences of symmetry in the matrix, the matrix coordinates were rearranged to yield
the primary matrix which is shown below, including values which were interpolated on the
basis of likelihood and alphabetical sequence.
2d Letter
9
C
K
X
S
D
M
Z
T
F
P
N
G
R
B
H
V
L
J
W
H
A1
AA
AB
AC
AD
AE
AF
AG
AH
AI
AK
AL
AM
AN
AO
AP
AR
AS
AT
AU
B
AV
m
AY
B2
BA
BE
BI
BL
BO
BR
BS
BU
BY
C3
CA
CC
CE
CH
Cl
CK
M
CL
CO
CR
CT
CU
CY
Db
DA
DB
DC
DD
DE
DF
DG
DH
DI
DL
DM
DN
DO
T
DP
DQ
DR
DS
DT
DU
DV
DW
DY
E5
EA
EB
EC
ED
EE
EF
EG
EH
El
EK
D
EL
EM
EN
EO
EP
EQ
ER
ES
ET
EU
EV
EW
EX
EY
EZ
f6
FA
FE
FF
F
FI
FL
FO
FR
FS
FT
FU
FY
G7
GA
GE
GF
GH
GI
GL
GM
GN
GO
GP
N
GR
GS
GT
GU
GY
H8
HA
HB
HC
HD
HE
HI
m
IL
IM
IN
10
IP
IR
IS
IT
IV
R
IW
IX
Jj£
JA
JE
JO
JU
K
KA
KE
KI
KO
L
LA
LB
LC
LD
LE
IF
LH
G
LI
LL
IM
IN
LO
LP
LR
IB
LT
LU
LV
LW
LY
M
MA
MB
ME
MI
MM
P
MO
MP
MR
MS
MT
MU
MY
N
NA
NB
NC
ND
NE
NF
NG
NH
NI
NL
NM
NN
W
NO
NP
NQ
NR
NS
NT
NU
NV
NW
NY
0
OA
OB
OC
OD
OE
OF
OG
OH
01
L
OK
OL
OM
ON
00
OP
OR
OS
OT
OU
OF
OW
OX
OY
P
PA
J
Q
QU
R
RA
RB
RC
RD
RE
RF
RG
Q
RH
RI
RL
RM
RN
RO
RP
RQ
RR
RS
RT
RU
RY
S
SA
SB
SC
SD
SE
X
SF
SG
SH
SI
SL
SM
SN
SO
SP
SQ
SR
SS
ST
SU
SW
SY
T
TA
TB
TC
C
TD
TE
TF
TG
TH
TI
TL
TM
TN
TO
K
<3
UL
VE
z
YC
By comparison with other messages in the same period, and with messages in subsequent
periods, it was possible to recover the values inside the matrix in their entirety, as follows:
10-11
CONFIDENTIAL
CONFIDENTIAL
REF ID : A56895
A
AA
AB
AC
AD
AE
AF
AG
AH
AI
AK
AL
AM
AN
AO
AP
AR
AS
AT
AU
AV
AW
AY
B
BA
BE
BI
BL
BO
BR
BT
BU
BY
C
CA
CC
CE
CH
Cl
CK
CL
CO
CR
CT
CU
CY
t>
DA
DB
DC
DD
DE
DF
DG
DH
Dl
DL
DM
DN
DO
DP
DQ
DR
DS
DT
DU
DV
DW
DY
E
EA
EB
EC
ED
EE
EF
EG
EH
El
EJ
EL
EM
EN
EO
EP
EQ
ER
ES
ET
EU
EV
EW
EX
EY
EZ
F
FA
FC
FE
FF
FI
FL
FO
FR
FS
FT
FU
FY
G
GA
GC
GE
GF
GG
GH
GI
GL
GN
GO
GP
GR
GS
GT
GU
GW
H
HA
HB
HC
HD
HE
HF
HI
HL
HM
HN
HO
HR
HS
HT
HU
HY
i
IA
IB
IC
ID
IE
IF
IG
IK
IL
IM
IN
10
IP
IR
IS
IT
IV
IX
IZ
J
JA
JE
JO
JU
K
KA
KE
KI
KS
L
LA
LB
LC
LD
LE
LF
LG
LI
LL
LM
LN
LO
LP
LR
LS
LT
LU
LV
LW
LY
M
MA
MB
KC
ME
MI
MM
MO
MP
MR
MS
MT
MU
MY
N
NA
NB
NC
ND
NE
NF
NG
NH
MI
NK
HL
NM
NN
NO
NP
NR
NS
NT
NU
NV
NW
NY
0
OA
OB
OC
OD
OE
OF
OG
OH
01
OK
OL
OM
ON
00
OP
OR
OS
or
OU
ov
OW
OX
OY
P
PA
PE
PF
PH
PI
PL
PM
PN
PO
PP
PR
PS
FT
PU
PY
Q
QU
R
RA
R3
RC
RD
RE
RF
RG
RH
RI
RL
RM
RN
RO
RP
RR
RS
RT
RU
RV
RW
RY
S
SA
SB
SC
SD
SE
SF
SG
SH
SI
SK
SL
SM
SN
SO
SP
SR
SS
ST
SU
SW
SY
T
TA
TB
TC
TD
TE
TF
TG
TH
TI
TL
TM
TN
TO
TP
TR
TS
TT
TU
TW
TY
TZ
U
UA
UB
UC
UD
UE
UG
UI
UL
UM
UN
UP
UR
US
UT
V
VA
VE
VI
VO
W
WA
WE
WH
WI
WL
WN
WO
WR
WY
X
XA
XC
XE
XF
XI
XN
XP
XT
Y
YA
YB
YC
YD
YE
YF
YG
YH
YI
YL
YM
YN
YO
YP
YR
YS
YT
YW
Z
ZA
ZE
ZI
It will be noted that the matrix contains the 26 letters, and 374 of the highest frequency
digraphs. When encrypting numbers, the cipher value for 1 is the cipher equivalent of
Ap , the cipher value for 2 is the 66 c for Bp, etc. , to 0p = 09 c (Jp).
15. In the matrix coordinates for the first key period, the non- random pheno-
mena in the grouping of the coordinate letters was noticed, suggesting that some
systematic method for producing these sequences was used. It evolved that these se -
quences were derived by simple columnar transposition using the following rectangles: ■
For the rows; For the columns:
HDRLC
B F G J K
M N P Q S
T V W X Z
Q S T N B L
C D F G H J
KHPRVW
X z
Thus the key words for the first period are HYDRAULIC and QUESTIONABLY (with,
of course, the vowels omitted) for the row and column coordinates, respectively.
IV - CONTINUITY OF KEY CHANGES; SUMMARY
16, Having solved the CALOX system for the first period (12-18 Dec), the second
period (19-26 Dec) was easily solved by the discovery of a pair of cross-key isologs on
19 December; the third period (27-31 Dec) was speedily solved by means of a signature
crib; while the fourth period (beginning on 1 Jan) had to be solved by the general method
of digraphic frequencies and digraphic idiomorphs. The row and column key words for
the second period were COPYRIGHTED and DOCUMENT; for the third period, CHIMPANZEE
and MANDRILL; but for die fourth period the same key word, MNTVD (Montevideo?), was
used for both die row and column coordinates. The coordinate sequences were derived by
simple columnar transposition, as in the first period.
10-12
CONFIDENTIAL
REF ID: A56895
CONFIDENTIAL
17. If the enemy has found that two different sequences for the row and column
coordinates is too inconvenient cryptographically and therefore continues to use the single
key word procedure started ill the fourth period, a statistical technique has been devised
for establishing the identity of some (or even all) of the letters of the coordinates, based
on a consideration of the relative frequencies of die ciphertext letters. Tills technique
is founded on the fact that in a single key word procedure the combination of row 19 and
column 19 of the basic matrix will yield a low frequency cipher letter, as will the
combinations of row 20-column 20, and row 9-column 9; on the other hand, the combi-
nations row 17-column 17, row 5-column 5, row 13-column 13, and row 14-column 14
will yield high frequency cipher letters. With a single key word procedure being used,
the following is the expected descending frequency order of the twenty row-column
combinations:
17 5 13 14 1 8 18 15 4 3 12 16 G 11 7 10 2 9 20 19
Even if two key words are employed for the coordinates, a modification of the statistical
method is feasible, m those instances where any difficulty might be encountered in a
new key period. The statistical techniques and the methods of their employment wdl be
described in a later report.
18, No trouble is anticipated in keeping current with key changes in the CALOX
system; traffic should be readable now on the first day of a key change. If die enemy used
another set of 5 letters as nulls, instead of the vowels, the new nulls can be identified by
searching for and examining near-repetitions, as shown in par. 11, A similar procedure
would be used to identify a new number indicator, even though solution would not be
impeded by this latter factor, 1
19. The traffic analysis report on the CALOX traffic gives complete statistics on
the links on which CALOX is found, as well as a detailed summary on the number of mes-
sages intercepted, etc.
\
CONFIDENTIAL
10-13
CONFIDENTIAL
REF ID : A56895
(blahk)
REF ID: A5 68 95
, "faAjJ k *
- CQNFIDENTTA t r
NATIONAL SECURITY AGENCY
- - Washington 25, D. C.
COURSE
LESSON 8
‘ - • l . V
TEXT ASSIGNMENT
Military Cryptanalysis, Part I
i - - 1 -
Monoalphkbetic substitution with
irregular -length cipher units;
monome -dinome systems and others
Section X
V/ *- 4 »
1. Solve the following monome -dinome cryptogram and recover the
original matrix:
78131
7 6 7 8 4
31174 50078
7 6 3 4 3
47807
4 13 4 6
5 3 3 3 4
0 13 3 1 0 17 9 9
7 8 3 1 8
7 6 4 4 1
3 19 17
92478
a . • ¥
74179 10834
7603 3
5 5 7 2 3
40178
3 13 4 7
46554 65323
4 13 0 5
86131
3 M 6 7
3 0 3 4 5
7 7 7 8 7 4 8 7 6 3
7 7689
76072
7 6 7 4 7
8 8 12 3
11278 31788
76503
4 7 7 5 3
17807
6 7 9 2 1
0 7 2-7 6 07 3 10
'l 7 9 9 7
88878 ,
7 4 7 0 3
0 5 3 2 3
1 * 'i ^1 ii 7 TT r ; 7 v - - "”
1 5777.. 7 1034
m, A -V
7 V 3 7 1
*3 3 7 6 4
47117
37607 -
88390 00 6 " 6 IT
“ 3 3 3 0*0
0 3 9 8 5 *
7 9 5 3 1
3 15 3 3
V .
7 8~3 4 2 47800
1 - * ■ ' -0 ■< _ -
•1 7 2 3 0
7 5560
3 4 8 5 0
• « 4,
7 4 5 4 7
^ j. *± \ ' _
83189
• i-*. .
J
- H
f “ * *
X ^ J l*
"V* "V' •- _
VJ
- • V
U.
" Vl •
. ‘ ? » >
/ i. v* f • Am j
r .. 4 * i f ; • ? , “
*;• - T •'
' ‘
4
A
» £ s r * ' '*
j *■ * 1 « j » ’
* f *- i * * • . V**.
-
1 ▼
- - .
¥
— - « '7*“
T
1 1
- a
a 1 •" jT ■ 1 « 1 ^
- ■ » * • *•
. i
COMFIDENTIMr
1
CONFIDENTIAL
REF ID : A56895
2 . The following monorae -dlnome cryptogram la believed to contain the
probable word "DIVISION”. Solve the text and recover the original matrix:
17832
0 0 0 6 6
16927
80635
2 8 4 2 0
0 4 5 9 6
95220
01900
2 15 0 0
40563
2 6 7 4 6
1 2 5 7 6
80705
88123
5 3 9 2 1
3 1118
1 3 2 8 1
2 9 15 9
4 6 4 6 5
61576
5 2 8 4 4
9 0 0 3 3
9 4 5 2 6
5 9 4 0 0
2 5 2 8 4
3 0 0 3 2
00457
80758
80707
0 0 5 2 6
7 3 9 4 1
2 0 8 5 4
5 6 6 4 0
5 9 3 5 2
9 16 2 5
9 7 6 1 2
4 6 9 7 7
89125
0 5 9 4 5
2 2 0 0 8
4 1 4 0 1
5 112 9
3 17 0 2
91067
5 3 7 6 3
59062
3 8 0 7 1
6 7 0 0 3
8 4 6 7 0
0 4 2 6 7
7 8 5 7 9
2 0 0 8 4
17 9 19
6 0 2 6 6
4 3 5 9 5
6 5 6 9 7
00036
1 2 0 0 4
9 7 6 1 6
8 7 2 0 2
6 0 0 4 5
70787
0 5 9 7 1
2 6 12 2
8 12 0 0
1 9 0 0 3
0 0 8 4 1
76912
0 9 5 9 9
7 2 6 7 3
3 . The following cryptogram was intercepted on a link which has been
known to be passing traffic in two different monome -dlnome systems, one
Involving a matrix of the type shown in Fig. 75 of the text, the other
Involving a matrix of the type in Fig. 77 • Solve the text of the message
and recover the original matrix.
4 7 6 3 1
82870
1 4 6 2 8
3 12 7 4
1 2 7 4 1
1 6 2 6 3
16054
63152
8 4 6 6 2
6 0 7 3 6
97728
46198
4 6 9 7 2
13808
4 6 2 8 7
4 6 3 6 4
83788
7 2 8 4 6
6 0 8 4 6
28738
2 7 5 7 8
87073
1 8 2 7 9
6 2 7 3 6
9 7 4 6 2
83107
3 6 9 7 7
4 5 6 3 6
2 6 9 6 2
7 3 16 8
6 2 7 6 3
12138
0 8 4 6 2
8 7 3 1 6
0 6 3 7 9
82647
2 8 4 6 7
CONFIDENTIAL
2
_ \ _REF ID :A56895 -
CONFIDENTIAL
4. The following messages, intercepted on a link known to he passing
monome-dinome traffic, are believed to be isologs. Solve the texts and re-
cover the original matrices. * ‘ '
Message "A"
9 4 8 7 2
3 3 9 3 5.
61227
8 9 3 1 6
23405
0 9 0 7 9
43810
5 7 6,7 8.
9 3 .3 8 6
4 1 9 9 9
83809
08334
9 4 19 4
76279
99496
3 0 5 7 6
79 1.9,9
5 4 3 4 3
5 7 6 8 3
0 4 1 8 6
07981
4 3 3.4 9
83 5 2 9
\ % *
09638
—
Message "B"
9 4 3 7 8
119 3 5
62887
3 93 26
8 1 4 0 5
0 9 0 7 9
4 13 2 0
5 7 6 7 3
931.36
4 19 9 9
1 4 n w
81309
0 3 114
t ‘ 1
9 4 19 4
7 6 8 7 9
99496
10576
7 9 19 9
5 4 3 4 3
5 7 6 3 1
0 4 1 3 6
0 7 9 8 2
43149
3 15 8 9
09613
J i - * _ 9
CONFIDENTIAL
3
REF ID : A56895
C ONFIDE NTIAL
5. The following messages are believed to be isologous monome-
dinome ciphers. Solve the texts and recover the original matrices:
Message "A"
7 3 5 0 7
14 9 8 3
3 0 7 4 1
3 0 4 1 5
5 19 8 3
16361
0 7 9 0 1
3 5 0 3 9
3 6 7 1 3
5 6 2 9 6
43072
72171
6 2 9 6 8
3 4 3 3 9
7 4 2 9 2
7 4o65
09885
12316
59012
6 5 0 7 5
12316
8 0 7 7 2
10 12 1
0 4 3 9 8
4 5 8 0 7
8 9 2 1 6
7 4 2 9 2
3 2 5 6 4
9 2 1 6 3
7 3 4 8 4
7 8 0 1 7
01652
5 2 3 7 1
5 4 3 9 8
43098
5 2 3 7 1
9 7 0 5 6
98617
18921
3 7 7 9 8
5 6 5 7 1
58871
7 7 6 7 6
9 7 4 2 4
0 8 4 6 5
3 7 5 3 1
12890
50563
1 3 5 0 0
1 3 5 5 9
29092
5 6 3 9 8
63867
0 7 4 8 5
8 4 6 5 0
4 3 0 6 3.
85629
81798
26896
09804
9 3 3 1 2
9 8 4 6 0
7 4 3 7 9
3 3 12 4
58145
9 4i63
55406
62909
1 4 3 3 9
74180
06509
7 2 5 1 7
80036
3 9 8 5 8
42689
7 7 2 9 7
0 6 8 1 4
3 9 8 4 2
1 5 4 6 5 '
8 4 7 3 1
5 8 17 9
18085
7 3 6 4 0
7 9 8 7 5
89612
1 3 7 4 7
88716
Message "B 1
4
CONFIDENTIAL
” - REF ID: A5 6 8 95
CONFIDENTIAL
4 . The following messages, intercepted on a link known to he passing
monome-dinome traffic, are ‘believed to he isologs. Solve the texts and re-
cover the original matrices.
- * “ w » _ -» »_ z « - . * . ,
Message u A n
9 4 8 7 2
3 3 9 3 5
6 12 2 7
89316
2 3 4 0 5
09079
4 3 8 1 0
5 7 6 7 8
9 3 3 8 6
4 19 9 9
8 3 8 0 9
08334
9 4 19 4
76279
99496
3 0 5 7 6
7 9 1 9 9
54343
5 7 ,6 8 3
0 4 18 6
0798 l
4 3 3,4 9
8 3.5 2 9
09638
! 1
^"Message "B"
* s.
94378
119 3 5
62887
3 9 3 2 6
» » * »
8 1 4 0 5
, » ♦
09079
4 13 2 0
5 7 6 7 3
9 3 13 6
41999
81309
0 3 114
9 4 19 4
7 6 8 7 9
99496
10576
7 9 19 9
5 4 3 4 3
5 7 6 3 1
0 4 13 6
07982
43149
31589
- « ?
‘ 1 *■
09613
• 1
— A .
_i U .r kr
M * .1 . Jl
-W*J t * * ,■*»
• l a -
’ — V
* *
-- ■* *7'
^ ; 1 c
<* ^
•
t *
f
1 k ^ '
\ ‘ 1 f .' 5 '
r- - ^ >** * *•
;
. ..
CONFIDENTIAL
3
REF ID : A56895
CONFIDENTIAL
5. The following messages are believed to be isologous monome-
dinome ciphers. Solve the texts and recover the original matrices:
Message "A"
7 3 5 0 7
1 4 9 8 3
3 0 7 4 1
3 0 4 1 5
5 19 8 3
1 6 3 6 1
0 7 9 0 1
3 5 0 3 9
09885
12 3 16
5 9 0 1 2
6 5 0 7 5
12 3 16
8 0 7 7 2
10 12 1
0 4 3 9 8
0 16 5 2
5 2 3 7 1
5 4 3 9 8
4 3 0 9 8
5 2 3 7 1
9 7 0 5 6
9 8 6 1 7
3 7 5 3 1
1 2 8 9 0
5 0 5 6 3
1 3 5 0 0
1 3 5 5 9
2 9 0 9 2
5 6 3 9 8
0 9 8 0 4
9 3 3 1 2
9 8 4 6 0
7 4 3 7 9
3 3 12 4
58145
9 4 16 3
3 9 8 5 8
42689
7 7 2 9 7
0 6 8 1 4
3 9 8 4 2
1 5 4 6 5 '
8 4 7 3 1
Message "B"
36713 458
56296 892
43072 742
72171 325
62968 921
3 4 3 3 9 7 3 4
74292 780
7 4 0 6 5
0 7
18921
1 6
3 7 7 9 8
9 2
5 6 5 7 1
6 4
58871
6 3
7 7 6 7 6
8 4
9 7 4 2 4
1 7
0 8 4 6 5
63867 554
07485 629
84650 l 4 3
4306i 741
85629 065
81798 725
26896 800
06 58179
09 18085
39 73640
80 79875
09 89612
17 13747
36 88716
CONFIDENTIAL
4
REF ID : A56895
CONFIDENTIAL
6. Solve the following monome -dinome -trlnome cryptogram and recover
the original matrix:
6 17^5
0 4 12 0
4 3 9 5 0
4 3 2 3 8
6 5 3 3 2
0 6 3 8 2
0 15 0 3
2 0 6 8 2
616 6 1
2 0 4 3 6
5 3 5 1 3
17 15 0
6 8 4 12
1 9 2 0 3
1 6 2 0 4
3 8 5 4 3
1 2 0 4 3
2 0 15 0
3 5 3 5 0
1 2 3 3 5
4 5 0 3 9
4 4 17 1
2 0 18 6
5 0 9 2 9
78509
2 3 8 5 0
4 6 2 0 4
8 4 7 3 9
4 5 0 4 9
6 2 0 6 5
8 2 8 2 0
4 3 5 3 2
01561
9 3 2 3 1
6 5 1 8 4
7 15 3 3
5 3 8 4 2
0 4 5 4 1
6 2 4 5 3
3 2 0 4 3
8 5 4 2 1
6 8 5 6 4
7« . Solve the following unillteral -biliteral cryptogram, and recover
all keys:
P V 0 Y A
C K R T E
A U 0 0 D
K N W 0 I
BKEIA
U B T A P
W 0 I D 0
OBKRT
A E N X B
T A E B G
Y A E U I
ENLCT
EOBZF
H 0 OB L
YIEBO
U U 0 N T
B X P X R
MIBKA
C W 0 I E
P KC 0 P
V A Y E P
TE1BM
PKSGE
Y A 0 D K.
UEDLR
Z E Y A H
0 C W U Y
A'TIPKP
M E 0 I A
C V P W Y
R W 0 Y C
W A P W 0
I Y A 0 R
W.s V C H
E I R V C
KYYPK
0 I C K Y
H W 0 D H
R K D 0 E
A E B X U
EBXBH
E Y A B T
E U C W R
0 R T D W
PH 0 A 0
POUDG
R K C V Y
0 K Z B 0
U EH T X
CONFIDENTIAL
5
REF ID : A56895
CONFIDENTIAL
8. The following c ry p t ogram, enciphered In a Playfair -type di-
graphic -monographic system, is suspected to begin with the probable
stereotype "MORNING REPORT FOR MONDAY NOVEMBER TWENTY FIRST." Solve
the text and recover all keys.
A Q T I N
J F Q H Q
PTLOP
TAQ8K
I V A T X
C J E H Q
FZKHB
ZOEIB
PEPPQ
QTDHK
HLROP
TBVBZ
P Z P R 0
L V T P 0
0 AEEQ
M P 0 A Y
QMEHF
K R R K Q
HQKKH
RJHPH
B J C HD
K Z Y8 R
KQBCA
K QR Y Q
MCQ6G
AEEQN
PRYQN
Q X 0 L V
QIJTE
MQKED
A H C T M
K Q V 0 0
AEEQT
A X Q V P
K M R J N
P H E J C
M D K Z Y
3BXLT
LOCKX
C X K T P
«
9. The following cryptogram was enciphered in a dinome -trinome
digraphic system employing matrices similar to those in Figs . 90a and
b, except that the Internal numerical sequences have been changed. The
message is suspected to end with the signature VINCENT ANDERSEN COL INF.
Solve the text and reconstruct the matrices Involved.
71665
7 3 3 3 0
1 3 9 2
2 5 2 2 1
3 9 2 2 5
8 6 7 6 5
0 18 0 2
6 0 9 4 0
4 4 26 3
12 5 14
47303
6 0 7 3 3
9 6 10 4
7 0 2 7 3
7 2 0 2 7
5 3 0 7 2
8 5 7 3 5
3 9 5 1 8
4 2 3 0 1
0 7 8 2 4
2 2 13 2
Y1923-
5 19 0 3
5 1 6 6 3
9 2 5 6 9
0 9 4 0 2
7«709
*► 0 3 5 3
01078
2 19 4 6
9 5 7 5 5
85962
4 2 2 1 3
* 7 1 9 7
65187
2 6 7 5 2
7 4 0 9 7
5 5 7 3 4
86919
61182
81051
0 2 7 1 9
85196
5 7 3 9 2
2 0 0 8 5
3 2 5 3 6
7 5 17 1
9 2 5 7 7
6 3 4 9 4
3 5 2 3 4
4 5 067
1 9 3 4 9
22522
0 4 7 1 4
4 1 0 4 5
2 2 2 1 6
5 7 5 08
1 7 5 3 7
16223
9 3 14 4
24586
3 4 9 4 4
8 2 5 0 6
CONFIDENTIAL
6
CONFIDENTIA L
REF ID : A56895 _
v
. . - l f*
10. The following cryptogram, based on a Morse code system, is sus-
pec ted to begin with a
spelled-out
number. Solve it and recover all ]
7 1^30
62809
1 8 5 9 2
3 5 6 0 7
6 15 7 2
0 4 9 5 3
7 9 0 1 2
8 7 5 4 8
6 5 9 8 3
0 4 0 3 7
9 5 3 2 7
3 0 7 . 5 1
3^904
5 6 5 6 4
2 0 8 1 3
0 1258
1 6 4 0 8
9 7 15 6
6 4 5 9 7
6 0 4 1 0
8 3 15 9
3 4 7 0 2 _
68032
9 5 3 5 7
2 5 17 3
02589
4 15 8 2
60360
9 17 5 4
•' > *
rONFTDFNTIAL
7
REF ID : A56895
CONFIDENTIAL
(blank)
CONFIDENTIA L
REF ID: A5 68 95"
mm-
2* The following three messages were selected from a volume of
Converter M-209 traffic because they were enciphered with the same
message indicators, a serious violation of cryptographic security.
It is furthermore suspected that stereotypic beginnings may have
been used in the drafting of the three messages. Solve the messages,
and submit the plain text to Message "A".
Message "A”
E E L 0
U
I S E L
C
Z YSXL
H 0
S R M
C
X
U
XKK
K
X T F C
S
J G L N
0
IJNaF
R U Z
T
T
N
0 M K
P
M M D P
E
K I H S
R
J H V Z C
C F C
0
H
Z
N B T
D
K Q M M
G
EELO
U
ISELC
Message "B 1
ii
EELOU
I
SEE
i T
E
C Z G E
E >J
V
E G
L J X
Z
U
D T
0
M Y W M W
B
C X V
K
D K C Z
u
R B
ABO
A
B
L S
Z
I Y L S C
S
R R W
P
ISON
w
E E
LOU
I
S
E E
E
Message "C"
EELOU
ISELC
P I F M C
Z I J
Y P
B H W G K
R t' F £ A-
C VC
e
W Z E B y/
B X Q I B
D V W U E
Z K K
T P
DKHXT
EEYAE,
D V E G L
B D I R P
K T S
G 0
M J Z Z F
EELOU ISELC
2
CONflDCNT I /M r
SECURITY INFORMATION
1
12 2 3 3 4 4
60 5 0 5 01
A
YDSQPKBLAJNCGMWEZXGUROIHFV
A
YDSQPKBLAJN C©M WE Z X® U ROIHPV
B
IQLJ$GDAU*RHKFECBWNXMVZOSY
T
WZETRQLCMBKO D(g)N X F A Y<g>V SP JIG
C
RVBLTOMVJGDXWUKNSHFEZQAPYC
N
hxafusrmonclpe®oygbz(Dwtqkj
D
Z JRKKTHEB7U S ILQFDCXOYNWAPT
1
KIYBGVTSNEODMQ F@P Z H C P .( 3 )X URL
E
AETXDNVQQXLIFZYWMPUJHGBSCR
J
MLJZCHWUTQFPENRGKQAIDBKYVS
F
FWGVEIXBHRZU SBPMJDCAQTYNLK
Q
TNMKADIXVUPGQFOSHLRBFECLZW
G
LGXHWFJYCISAVTCQN*EDBRUZOM
X
XUONLBEJYWVQHRGPTIMSCKFDMA
H
SBFUYEOWRPYMJGAZXNQVKIHCTD
M
BYVPOMCFKZXWRISHQUJNTDLGEN
I
XIYBGVTSNEODMQFJPZHCAJXURL
Z
OCZWQPNDGLAYXSJTIRVXOUEMHF
J
MLJZCHWUTOFPENRGKQAIDBXYVS
L
GPDAXRQOEHMBZYTXUJSWLPVFN I
[1
XUONLBEJYWVQHRGPTIMSCKFDMA
S
JHQEBYSRPFINCAZULVKTXMQWG 0
L
GPDAXRQOEHMBZYTKU JSWLPVFNI
X
PKIRFCZTSQGJODBAVMWLUYNRXH
M
BYVPOMCFKZXWRISHQUJNTDLGEN
B
IQLJSGDAU*RHKPECBWNXMVZOSY
N
HXAFUSRMDNCLPEIOYGBZIWTQKJ
m
ZJRMKTHEBVUSILQFDCXOYNWAPT
0
NMHYIXGKZDJTBWU DROLFECSVAP
R
UAKSNLUIFCWVTJMRGEDYPZOXBQ
P
V F U D H W A'g QYTRAOLIC*ZPSXKKJE
C
RVBLTOMVJGDXWUKNSHFEZQAPYC
‘S'
TNMKADIXVU PGQFOSHLRBFECLZW
U
DSWCMUPNWKHEYXVLOTIGFARBQZ
R
UAKSNLUIFCWVTJMRGEDYPZO.XBQ
E
AETXDNVQOXLI FZYWMPUJHGBSC R
S
JHQEBYSRPFIKC AZULVKTXMQWGO
H
SBFUYEOWRPYMJGAZXNQVKIHCTD
T
WZETRQLCMB KODHNXFAYHV SPJ IG
ES
ETCGVZFPXSQZNKHBAYORWLJ IDU
U
DSWCMUPNWKHEYXVLOTIGFARBQZ
p
VFUDHWAGQYTRAOLIC*ZPSXMKJE
V
ETCGVZFPXSQZNKHBAYORWLJIDU
F
FWGVEIXBHRZUSBPMJDCAQTYNL K
w
Q 0 N I ZJYHL#EKU CX VESPMGFDTWB
G
LGXHWFJYCISAVTCQN*EDBRUZOM
X
PKXRFCZTSQGJ OOBAVHWLU YRRXH
0
NHHYIXGKZDJTBWUDROLFECSVAP
Y
CRPOJ AXZIMBFLVDYWFTQNHGEUX
W
QONIZJYHL*EKUCXVESPMG FDTWB
Z
PKIRFCZTSQGJODBAVM'WLUYNRXH
Y
CRPOJAKZIMBFLVDYWFTQNHGEU X
-ts*
OCZWQPNDGLAYXSJTIRVKQUEMHF
Fig 1 . Enciphering alphabets 16-41 - Purple values
consitute the partial alphabets obtained through depth
reading; red values are derived by examination of the
basic c .pher=*text sequences (using the entire set of
100 partial alphabets) -
Fig 2 ., The Friedman square for the fast
rotor, obtained by rearranging the rows of
Fig 1 (using the isomorphic patterns of the
rows) so as to yield identical sequences for
all the diagonals.
CONFIDENTIAL
16 42 63 94
5
aJ
5?
A
B
C
D
E
F
G
H
I
J
K
L
M
N
0
P
Q
R
S
T
U
V
W
X
y
z
Ys W P A
A
l\l S I
B
R C X H £
C
Z N F T
D
A X Y L
E
F T A W
F
L P K S
G
S E B M
H
K V Z 0
I
MsG L U
J
X \ Q N
X
G AX) C
L
B Q T G
M
H D U X
N
WORE
0
V Y W D
P
T L J H
Q
U K E P
R
Jkl G V
w\c J
S
T
B s n h y!
U
E R V K
V
Q Z N F
W
P U X Q
X
C B I B
Y
0 F D Z
Z
IMP
I JS
ROM
ZHPH
A X Y
F T A
LPK
S E B
K V Z
HGL
X H Q
GAO
B Q T
H D U
NOR
V Y W
T L J
UKB
JIG
W M C
D S H
E R V
Q Z N
P U X
G B I
0 P D
W
E
F
B
R
N
Fig 3 o Enciphering alphabets 16, 42. 68, Fig 4 A fragment of the Friedman square for the
and 94o These alphabets, spaced at intervals medium rotor, with one of the repeating diagonals ex-
of 26 along the keying cycle, resulted from tended <
four successive positions of the medium rotor
at points along the cycle where the fast rotor
had returned to its initial position.. Note
that a diagonal chain may be completed, using
alphabets 16, 42, and 68.
ENCIPHERING ALPHABETS, "ZEBAB" PROBLEM
1 1 2 2 3 3 4 4.5
5050505050
A|V T J M R G E D Y P Z QYDSQPKBLA NC MW E Z X G U R 0 HFVWZETR L C m!a
B LJ HKPE X 7 OS SR B
CZ KHB Y 0 R W ID R L OM JG XWU NSHFEZ P-YCCRP J ZIC
DQH GPT MSCKF ZJ KT EB LQF CXOYNW P NMHYIXGKZD
BFLVDYWFTQNHGEUXAETXDNVQOXL FZYWMPUJHGBSCRXUONLBEJYE
9 FRAOL PSX JEFWGVE B R S PMJ C TYN K K DI F
GOHXF H PJ XHFJYC A V T C BRUOM R Z C-
KG Q SH RB ECLZW F EOW M G X Q? I T VZP XH
IN AZULV TXMQWGOKIYBGVTSNEODMQFJPZHCA XURLV U DHWAGQI
J R J
IViyiK E K K
,L ODB VM XH QOEHM TX J5WLP NIA T DN OL
HP N 'GKQ D V BYVPO CFXZXWRISH U TDLG HQ I YH M
N WUKN H F E Z Q A P Y C H X A F U S R M D N C L P E I 0 Y G B Z I W Q K J D S W C M U P N W N
0 JGAZX VXIHCTDNMHYI G K Z D J T B W U D R 0 L F E G V A P 0 C Z W Q P N D G 0
PIFZYWM UJ GBSC F DHW QYTR LI S K 3Q X L P
Q CVS K V G S Q
RCGMWEZXGURO H F V U A K S N L U I F C W V T J M R G E D Y P Z 0 X B Q K I Y B VTSNR
^ SY SJ IR KO EMHFJHQEBYSRPFINCAZULV T X M Q W G 0 I Q L J S G AUS
WR S QU JNTDLGENWZETRQLCM KODH XFAYH SPJIGMLJZCHWUT
A V C N EDB Z
Y X S P F
U J L
X
B W Q X
Z MD WCMUPNWKHEYXV
F E F
L
0 IGF RBQZSBF YE R
Y IV V
S P D R T B
L I
G U Y 0 F
W
WUD OLFECSVAPOCZWQPNDGLAYXSJTIRVXOUEMHFFWGVEIXBH
NATIONAL SECURITY AGENCY
Washington 25, D. C.
"TAN" PROBLEM
(A problem in plaintext recovery from a shallow depth In a Baudot
system)
Training Division
9 November 1953
International Teleprinter Code
UPPER
CASE
weather symools
D
0
0
B
□
B
B
B
□
a
B
B
.
□
□
□
B
□
□
□
B
0
B
B
□
B
B
H
Ui
O
2
i/i
h-
u.
5
a
tj
t
5
C
COMMUNICATIONS
0
y
B
□
□
U
□
□
□
S
B
B
•
B
□
□
B
□
□
□
B
a
a
□
H
□
El
E
LOWER CASE
D
i
a
a
D
D
D
D
D
B
B
B
1
B
I
B
fl
B
B
B
fl
b
a
fl
Z
1
a;
o
|
1
□
B
B
□
B
□
B
fl
B
□
B
B
fl
B
B
B
□
B
B
B
□
B
Q
□
o
fl
fl
fl
□
□
z
•
o
B
B
B
B
B
B
_
_
□
B
B
B
Z
B
B
B
B
O
i
B
□
FEED HOLES
□
a
□
□
□
B
□
□
5
□
□
□
□
P
□
□
□
□
a
□
□
□
M
□
□
□
0
o
o
□
□
□
3
■
u
0
B
B
B
B
0
0
B
B
B
0
B
B
B
B
B
B
B
B
B
fl
B
o
J
B
B
B
4
■
a
0
B
B
B
i
B
B
B
0
B
B
B
B
B
B
B
B
o
fl
O
B
□
5
0
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
121
2
o
o
0
B
B
B
Vernara Encipherment Table
e 2
A
B
c
D
E
F
G
H
I
J
K
L
M
N
0
P
Q
R
s
T
U
V
w
X
Y
Z
2
3
4
5
6
7
A
4
S
L
Y
X
Z
I
7
G
Q
W
C
6
T
3
R
J
P
B
N
2
5
K
E
D
F
U
0
A
V
M
H
B
S
4
7
K
U
J
M
L
6
F
D
H
G
R
V
T
z
N
A
P
E
0
Y
2
W
Q
X
5
B
3
I
C
C
L
7
4
0
T
M
J
S
Q
G
V
A
F
X
D
U
i
2
H
E
P
K
5
N
3
6
R
Y
C
W
Z
B
D
Y
K
0
4
Q
2
N
5
T
X
B
3
R
G
C
6
E
M
W
I
Z
7
S
J
A
U
F
L
D
H
P
V
E
X
U
T
Q
4
W
3
R
0
Y
Z
N
5
L
I
7
D
H
2
C
B
6
F
A
J
K
S
G
E
M
V
P
F
Z
J
M
2
W
4
7
I
H
B
X
6
C
V
R
3
S
0
Q
5
Y
N
E
K
U
A
D
P
F
T
L
G
G
I
M
J
N
3
7
4
Z
A
C
R
Q
B
D
X
W
L
K
6
Y
5
2
P
0
T
H
V
E
G
U
S
F
H
7
L
S
5
R
I
Z
4
F
6
3
B
Q
U
W
X
M
E
C
2
N
Y
0
P
V
G
T
K
H
D
J
A
I
G
6
Q
T
0
H
A
F
4
L
P
J
S
Y
E
K
C
W
M
D
V
U
R
3
N
7
5
X
I
2
B
Z
J
Q
F
G
X
Y
B
C
6
L
4
2
I
7
0
N
5
A
V
Z
3
W
R
U
D
E
S
K
T
J
P
H
M
K
w
D
V
B
Z
X
R
3
P
2
4
5
N
M
7
I
U
G
Y
6
Q
C
A
F
S
E
J
H
K
L
T
0
L
C
H
A
3
N
6
Q
B
J
I
5
4
Z
E
Y
2
G
U
7
X
R
W
V
T
0
M
P
D
L
K
F
S
M
6
G
F
R
5
C
B
Q
S
7
N
Z
4
K
2
Y
H
D
I
W
3
X
T
V
p
L
0
U
M
E
A
J
N
T
R
X
G
L
V
D
U
Y
0
M
E
K
4
J
S
3
B
P
A
H
F
6
C
I
5
7
Q
N
Z
W
2
0
3
V
D
C
I
R
X
W
E
N
7
Y
2
J
4
Z
T '
F
5
Q
6
B
H
G
L
P
M
A
0
S
U
K
P
R
T
U
6
7
3
W
X
K
5
I
2
Y
S
Z
4
V
A
N
B
C
Q
G
H
M
0
L
F
P
J
D
E
Q
J
Z
I
E
D
S
L
M
C
A
U
G
H
3
T
V
4
5
F
0
K
P
2
Y
X
B
W
N
Q
R
7
6
R
P
N
2
M
H
0
K
E
W
V
G
U
D
B
F
A
5
4
T
S
L
J
I
7
6
3
C
Z
R
Q
Y
X
S
B
A
H
W
2
Q
6
C
M
Z
Y
7
I
P
5
N
F
T
4
R
X
3
D
U
K
J
E
V
S
0
G
L
T
N
P
E
I
C
5
Y
2
D
3
6
X
W
A
Q
B
0
S
R
4
7
Z
M
L
G
V
H
J
T
F
K
U
U
2
E
P
Z
B
Y
5
N
V
W
Q
R
3
H
6
C
K
L
X
7
4
I
J
S'
F
D
A
M
U
G
0
T
V
5
0
K
7
6
N
2
Y
u
R
C
W
X
F
B
Q
P
J
3
Z
I
4
L
M
H
T
G
S
V
A
E
D
W
K
Y
5
S
F
E
P
0
R
U
A
V
T
6
H
G
2
I
D
M
J
L
4
Z
B
X
Q
7
w
C
N
3
X
E
2
N
J
A
K
0
P-
3
D -F
T
V
C
G
H
Y
7
U
L
S
M
Z
4
Q
W
B
I
X
6
5
R
Y
D
W
3
A
J
U
T
V
N
E
s
0
P
I
L
M
X
6
K
G
F
H
B
Q
4
2
Z
C
Y
7
R
5
Z
F
Q
6
U
K
A
H
G
7
S
E:
M
L
5
P
0
B
3
J
V
D
T
X
W
2
4
Y
R
Z
N
C
I
2
U
X
R
F
S
D
V
T
5
K
J
P
0
7
M -L -W -C
E
H
A
G
Q
B
Z
Y
4
6
2
I
3
N
3
0
5
Y
L
G
P
E
K
X
T
H
D
U
Q
A
F
N
z
V
J
M
S
7
I
C
R
6
4
3
B
2
W
4
A
B
C
D
E
F
G
H
I
J
K
L
M
N
0
P
Q
R
S
T
U
V
W
X
Y
Z
2
3
4
5
6
7
5
V
3
W
H
M
T
U
D
2
P
L
K
E
Z
S
J
R
Q
0
F
.G
A
c
6
7
N
I
B
5
4
X
Y
6
M
I
z
P
V
L
S
J
B
H
T
F
A
W
U
D
7
Y
G
K
0
E
N
5
R
C
3
2
6
X
4
Q
7
H
C
B
V
P
G
F
A
Z
M
0
S
J
2
K
E
6
X
L
U
T
D
3
R
5
I
N
W
7
Y
Q
4
CONFIDENTIA L
’ ."TAH" PROBLEM
The following messages represent three radioprinter intercepts
obtained on the same day. From analysis of prervious traffic, it is
known that the first four letters of each message constitute the indi-
cator; a single space is used between all words, and a message center
idiosyncrasy is the use of the doubled CR CR LF LF for the carriage
return-line feed operation.
In the representation of the six special functions, the following
notation has been used:
Figures 2
Space 3
Letters 4
Line feed 5
Blank 6
Carriage return 7
It is suspected that one of the messages Intercepted in the morn-
ing contains the probable vord REPORT. Solve the texts of the morning
messages; and, after correctly juxtaposing the third message along the
keying cycle, recover the plain text to the third message.
Message "A”
EDA BE IZX
0930Z
17 DEC
IVIVP
LWPZX
EIT02C
UBHVZ
EEKWF
mfn4f
-P-e
26SBK
POJLV-
XEB5F
VD6F3
CTOMV
YEYUV
QXI2H
HCW5C
KSK02
YBIHC
FHB5-TC
C423G
KXVTH
I4AVS
SUG06
Message "B”
EDA DE IZX
0945Z
17 DEC
IVTVTI
PEEKF
F7CIU
HUIAP
EkVP7
RIVEF
fine
UKGEII
fc-YflU
UZIW3ST
GI2TY
IZVEZ
ud6us
67 E 5 Z
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CONFIDENTIAL
REF ID : A56895
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